diff --git a/.github/workflows/linux_blas.yml b/.github/workflows/linux_blas.yml
index 17ff957bd2db..b90e32d00b32 100644
--- a/.github/workflows/linux_blas.yml
+++ b/.github/workflows/linux_blas.yml
@@ -10,9 +10,27 @@ name: BLAS tests (Linux)
 #   - openblas32_stable_nightly:
 #         Uses the 32-bit OpenBLAS builds, both the latest stable release
 #         and a nightly build.
-#
-# TODO: coverage here is limited, we should add non-OpenBLAS libraries and
-#       exercise the BLAS-related build options (see `meson_options.txt`).
+#   - openblas_no_pkgconfig_fedora:
+#         Test OpenBLAS on Fedora. Fedora doesn't ship .pc files for OpenBLAS,
+#         hence this exercises the "system dependency" detection method.
+#   - flexiblas_fedora:
+#         Tests FlexiBLAS (the default on Fedora for its own packages), via
+#         pkg-config. FlexiBLAS allows runtime switching of BLAS/LAPACK
+#         libraries, which is a useful capability (not tested in this job).
+#   - openblas_cmake:
+#         Tests whether OpenBLAS LP64 is detected correctly when only CMake
+#         and not pkg-config is installed.
+#   - netlib:
+#         Installs vanilla blas/lapack, which is the last option tried in
+#         auto-detection.
+#   - mkl:
+#         Tests MKL installed from PyPI (because easiest/fastest, if broken) in
+#         3 ways: both LP64 and ILP64 via pkg-config, and then using the
+#         Single Dynamic Library (SDL, or `libmkl_rt`).
+#   - blis:
+#         Simple test for LP64 via pkg-config
+#   - atlas:
+#         Simple test for LP64 via pkg-config
 
 on:
   pull_request:
@@ -87,3 +105,253 @@ jobs:
       run: |
         pip install pytest pytest-xdist hypothesis typing_extensions
         spin test -j auto
+
+
+  openblas_no_pkgconfig_fedora:
+    if: "github.repository == 'numpy/numpy'"
+    runs-on: ubuntu-latest
+    container: fedora:39
+    name: "OpenBLAS (Fedora, no pkg-config, LP64/ILP64)"
+    steps:
+    - name: Install system dependencies
+      run: |
+        dnf install git gcc-gfortran g++ python3-devel openblas-devel -y
+
+    - uses: actions/checkout@8ade135a41bc03ea155e62e844d188df1ea18608 # v4.1.0
+      with:
+        submodules: recursive
+        fetch-depth: 0
+
+    - name: Install dependencies
+      run: |
+        pip install -r build_requirements.txt
+        pip install pytest hypothesis typing_extensions
+
+    - name: Build (LP64)
+      run: spin build -- -Dblas=openblas -Dlapack=openblas -Ddisable-optimization=true
+
+    - name: Test
+      run: spin test -- numpy/linalg
+
+    - name: Build (ILP64)
+      run: |
+        rm -rf build
+        spin build -- -Duse-ilp64=true -Ddisable-optimization=true
+
+    - name: Test
+      run: spin test -- numpy/linalg
+
+
+  flexiblas_fedora:
+    if: "github.repository == 'numpy/numpy'"
+    runs-on: ubuntu-latest
+    container: fedora:39
+    name: "FlexiBLAS (LP64, ILP64 on Fedora)"
+    steps:
+    - name: Install system dependencies
+      run: |
+        dnf install git gcc-gfortran g++ python3-devel flexiblas-devel -y
+
+    - uses: actions/checkout@8ade135a41bc03ea155e62e844d188df1ea18608 # v4.1.0
+      with:
+        submodules: recursive
+        fetch-depth: 0
+
+    - name: Install dependencies
+      run: |
+        pip install -r build_requirements.txt
+        pip install pytest hypothesis typing_extensions
+
+    - name: Build
+      run: spin build -- -Ddisable-optimization=true
+
+    - name: Test
+      run: spin test -- numpy/linalg
+
+    - name: Build (ILP64)
+      run: |
+        rm -rf build
+        spin build -- -Ddisable-optimization=true -Duse-ilp64=true
+
+    - name: Test (ILP64)
+      run: spin test -- numpy/linalg
+
+
+  openblas_cmake:
+    if: "github.repository == 'numpy/numpy'"
+    runs-on: ubuntu-latest
+    name: "OpenBLAS with CMake"
+    steps:
+    - uses: actions/checkout@8ade135a41bc03ea155e62e844d188df1ea18608 # v4.1.0
+      with:
+        submodules: recursive
+        fetch-depth: 0
+    - uses: actions/setup-python@61a6322f88396a6271a6ee3565807d608ecaddd1 # v4.7.0
+      with:
+        python-version: '3.11'
+
+    - name: Install dependencies
+      run: |
+        pip install -r build_requirements.txt
+        pip install pytest pytest-xdist hypothesis typing_extensions
+        sudo apt-get install libopenblas-dev cmake
+        sudo apt-get remove pkg-config
+
+    - name: Build
+      run: spin build -- -Ddisable-optimization=true
+
+    - name: Test
+      run: spin test -j auto -- numpy/linalg
+
+ 
+  netlib:
+    if: "github.repository == 'numpy/numpy'"
+    runs-on: ubuntu-latest
+    name: "Netlib BLAS/LAPACK"
+    steps:
+    - uses: actions/checkout@8ade135a41bc03ea155e62e844d188df1ea18608 # v4.1.0
+      with:
+        submodules: recursive
+        fetch-depth: 0
+    - uses: actions/setup-python@61a6322f88396a6271a6ee3565807d608ecaddd1 # v4.7.0
+      with:
+        python-version: '3.11'
+
+    - name: Install dependencies
+      run: |
+        pip install -r build_requirements.txt
+        sudo apt-get install liblapack-dev pkg-config
+
+    - name: Build
+      run: |
+        spin build -- -Ddisable-optimization=true
+
+    - name: Test
+      run: |
+        pip install pytest pytest-xdist hypothesis typing_extensions
+        spin test -j auto -- numpy/linalg
+
+
+  mkl:
+    if: "github.repository == 'numpy/numpy'"
+    runs-on: ubuntu-latest
+    name: "MKL (LP64, ILP64, SDL)"
+    steps:
+    - uses: actions/checkout@8ade135a41bc03ea155e62e844d188df1ea18608 # v4.1.0
+      with:
+        submodules: recursive
+        fetch-depth: 0
+    - uses: actions/setup-python@61a6322f88396a6271a6ee3565807d608ecaddd1 # v4.7.0
+      with:
+        python-version: '3.11'
+
+    - name: Install dependencies
+      run: |
+        pip install -r build_requirements.txt
+        pip install pytest pytest-xdist hypothesis typing_extensions
+        pip install mkl mkl-devel
+
+    - name: Repair MKL pkg-config files and symlinks
+      run: |
+        # MKL 2023.2 works when installed from conda-forge (except for `-iomp`
+        # and `-tbb` pkg-config files), Spack, or with the standalone Intel
+        # installer. The standalone installer is the worst option, since it's
+        # large and clumsy to install and requires running a setvars.sh script
+        # before things work. The PyPI MKL packages are broken and need the
+        # fixes in this step. For details, see
+        # https://github.com/conda-forge/intel_repack-feedstock/issues/34
+        cd $Python3_ROOT_DIR/lib/pkgconfig
+        sed -i 's/\/intel64//g' mkl*.pc
+        # add the expected .so -> .so.2 symlinks to fix linking
+        cd ..
+        for i in $( ls libmkl*.so.2 ); do ln -s $i ${i%.*}; done
+
+    - name: Build with defaults (LP64)
+      run: |
+        pkg-config --libs mkl-dynamic-lp64-seq  # check link flags
+        spin build -- -Ddisable-optimization=true
+
+    - name: Test
+      run: spin test -- numpy/linalg
+
+    - name: Build with ILP64
+      run: |
+        git clean -xdf > /dev/null
+        pkg-config --libs mkl-dynamic-ilp64-seq
+        spin build -- -Duse-ilp64=true -Ddisable-optimization=true
+
+    - name: Test
+      run: spin test -- numpy/linalg
+
+    - name: Build without pkg-config (default options, SDL)
+      run: |
+        git clean -xdf > /dev/null
+        pushd $Python3_ROOT_DIR/lib/pkgconfig
+        rm mkl*.pc
+        popd
+        export MKLROOT=$Python3_ROOT_DIR
+        spin build -- -Ddisable-optimization=true
+
+    - name: Test
+      run: spin test -- numpy/linalg
+
+  blis:
+    if: "github.repository == 'numpy/numpy'"
+    runs-on: ubuntu-latest
+    name: "BLIS"
+    steps:
+    - uses: actions/checkout@8ade135a41bc03ea155e62e844d188df1ea18608 # v4.1.0
+      with:
+        submodules: recursive
+        fetch-depth: 0
+    - uses: actions/setup-python@61a6322f88396a6271a6ee3565807d608ecaddd1 # v4.7.0
+      with:
+        python-version: '3.11'
+
+    - name: Install dependencies
+      run: |
+        pip install -r build_requirements.txt
+        pip install pytest pytest-xdist hypothesis typing_extensions
+        sudo apt-get install libblis-dev libopenblas-dev pkg-config
+
+    - name: Add BLIS pkg-config file
+      run: |
+        # Needed because blis.pc missing in Debian:
+        # https://bugs.debian.org/cgi-bin/bugreport.cgi?bug=989076
+        # The alternative here would be to use another distro or Miniforge
+        sudo cp tools/ci/_blis_debian.pc /usr/lib/x86_64-linux-gnu/pkgconfig/blis.pc
+        # Check if the patch works:
+        pkg-config --libs blis
+        pkg-config --cflags blis
+
+    - name: Build
+      run: spin build -- -Dblas=blis -Ddisable-optimization=true
+
+    - name: Test
+      run: spin test -- numpy/linalg
+
+  atlas:
+    if: "github.repository == 'numpy/numpy'"
+    runs-on: ubuntu-latest
+    name: "ATLAS"
+    steps:
+    - uses: actions/checkout@8ade135a41bc03ea155e62e844d188df1ea18608 # v4.1.0
+      with:
+        submodules: recursive
+        fetch-depth: 0
+    - uses: actions/setup-python@61a6322f88396a6271a6ee3565807d608ecaddd1 # v4.7.0
+      with:
+        python-version: '3.11'
+
+    - name: Install dependencies
+      run: |
+        pip install -r build_requirements.txt
+        pip install pytest pytest-xdist hypothesis typing_extensions
+        sudo apt-get install libatlas-base-dev pkg-config
+
+    - name: Build
+      run: spin build -- -Dblas=blas-atlas -Dlapack=lapack-atlas -Ddisable-optimization=true
+
+    - name: Test
+      run: spin test -- numpy/linalg
+
diff --git a/.github/workflows/linux_musl.yml b/.github/workflows/linux_musl.yml
index 5f6da2ba765d..5c65a2b2e8b9 100644
--- a/.github/workflows/linux_musl.yml
+++ b/.github/workflows/linux_musl.yml
@@ -60,7 +60,7 @@ jobs:
         pip install -r build_requirements.txt -r test_requirements.txt
 
         # use meson to build and test 
-        spin build --with-scipy-openblas=64
+        spin build --with-scipy-openblas=64 -- -Duse-ilp64=true
         spin test -j auto
 
     - name: Meson Log
diff --git a/.github/workflows/macos.yml b/.github/workflows/macos.yml
index 0a7aa38c0ae7..8768b64e17cd 100644
--- a/.github/workflows/macos.yml
+++ b/.github/workflows/macos.yml
@@ -100,7 +100,7 @@ jobs:
         ccache -s
 
   accelerate:
-    name: Accelerate ILP64
+    name: Accelerate (LP64, ILP64)
     if: "github.repository == 'numpy/numpy'"
     runs-on: macos-13
     steps:
@@ -122,14 +122,15 @@ jobs:
         pip install -r build_requirements.txt
         pip install pytest pytest-xdist hypothesis
 
-    - name: Build NumPy against Accelerate (ILP64)
-      run: |
-        spin build -- -Dblas=accelerate -Dlapack=accelerate -Duse-ilp64=true
+    - name: Build against Accelerate (LP64)
+      run: spin build -- -Ddisable-optimization=true
 
-    - name: Show meson-log.txt
-      if: always()
-      run: 'cat build/meson-logs/meson-log.txt'
+    - name: Test (linalg only)
+      run: spin test -j2 -- numpy/linalg
 
-    - name: Test
+    - name: Build NumPy against Accelerate (ILP64)
       run: |
-        spin test -j2
+        spin build -- -Duse-ilp64=true
+
+    - name: Test (fast tests)
+      run: spin test -j2
diff --git a/azure-steps-windows.yml b/azure-steps-windows.yml
index ce11d06f5148..2c12287bbcfb 100644
--- a/azure-steps-windows.yml
+++ b/azure-steps-windows.yml
@@ -31,7 +31,7 @@ steps:
     }
     elseif ( Test-Path env:NPY_USE_BLAS_ILP64 ) {
         python -m pip install scipy-openblas64 spin
-        spin config-openblas --with-scipy-openblas=64
+        spin config-openblas --with-scipy-openblas=64 -- -Duse-ilp64=true
         $env:PKG_CONFIG_PATH="$pwd/.openblas"
         python -m pip install . -v -Csetup-args="--vsenv"
     } else {
diff --git a/meson.build b/meson.build
index 9ba86f393d6d..264160d132eb 100644
--- a/meson.build
+++ b/meson.build
@@ -12,8 +12,6 @@ project(
     'b_ndebug=if-release',
     'c_std=c99',
     'cpp_std=c++17',
-    'blas=openblas',
-    'lapack=openblas',
     'pkgconfig.relocatable=true',
   ],
 )
diff --git a/meson_options.txt b/meson_options.txt
index b126e22d1f63..588d0e404d22 100644
--- a/meson_options.txt
+++ b/meson_options.txt
@@ -1,13 +1,19 @@
-option('blas', type: 'string', value: 'openblas',
-        description: 'Option for BLAS library switching')
-option('lapack', type: 'string', value: 'openblas',
-        description: 'Option for LAPACK library switching')
+option('blas', type: 'string', value: 'auto',
+        description: 'Option for BLAS library selection. By default, try to find any in the order given by `blas-order`')
+option('lapack', type: 'string', value: 'auto',
+        description: 'Option for LAPACK library selection. By default, try to find any in the order given by `lapack-order`')
 option('allow-noblas', type: 'boolean', value: false,
         description: 'If set to true, allow building with (slow!) internal fallback routines')
+option('blas-order', type: 'array',
+        value: ['mkl', 'accelerate', 'openblas', 'flexiblas', 'blis', 'blas'])
+option('lapack-order', type: 'array',
+        value: ['mkl', 'accelerate', 'openblas', 'flexiblas', 'lapack'])
 option('use-ilp64', type: 'boolean', value: false,
        description: 'Use ILP64 (64-bit integer) BLAS and LAPACK interfaces')
-option('blas-symbol-suffix', type: 'string', value: '',
-        description: 'BLAS and LAPACK symbol suffix to use, if any (often `64_` for ILP64)')
+option('blas-symbol-suffix', type: 'string', value: 'auto',
+        description: 'BLAS and LAPACK symbol suffix to use, if any')
+option('mkl-threading', type: 'string', value: 'auto',
+        description: 'MKL threading method, one of: `seq`, `iomp`, `gomp`, `tbb`')
 option('disable-svml', type: 'boolean', value: false,
         description: 'Disable building against SVML')
 option('disable-threading', type: 'boolean', value: false,
diff --git a/numpy/core/src/common/npy_cblas.h b/numpy/core/src/common/npy_cblas.h
index dad9599f605e..596a7c68cedd 100644
--- a/numpy/core/src/common/npy_cblas.h
+++ b/numpy/core/src/common/npy_cblas.h
@@ -57,8 +57,21 @@ enum CBLAS_SIDE {CblasLeft=141, CblasRight=142};
 #define BLAS_FUNC_CONCAT(name,prefix,suffix,suffix2) prefix ## name ## suffix ## suffix2
 #define BLAS_FUNC_EXPAND(name,prefix,suffix,suffix2) BLAS_FUNC_CONCAT(name,prefix,suffix,suffix2)
 
-#define CBLAS_FUNC(name) BLAS_FUNC_EXPAND(name,BLAS_SYMBOL_PREFIX,,BLAS_SYMBOL_SUFFIX)
+/*
+ * Use either the OpenBLAS scheme with the `64_` suffix behind the Fortran
+ * compiler symbol mangling, or the MKL scheme (and upcoming
+ * reference-lapack#666) which does it the other way around and uses `_64`.
+ */
+#ifdef OPENBLAS_ILP64_NAMING_SCHEME
 #define BLAS_FUNC(name) BLAS_FUNC_EXPAND(name,BLAS_SYMBOL_PREFIX,BLAS_FORTRAN_SUFFIX,BLAS_SYMBOL_SUFFIX)
+#else
+#define BLAS_FUNC(name) BLAS_FUNC_EXPAND(name,BLAS_SYMBOL_PREFIX,BLAS_SYMBOL_SUFFIX,BLAS_FORTRAN_SUFFIX)
+#endif
+/*
+ * Note that CBLAS doesn't include Fortran compiler symbol mangling, so ends up
+ * being the same in both schemes
+ */
+#define CBLAS_FUNC(name) BLAS_FUNC_EXPAND(name,BLAS_SYMBOL_PREFIX,,BLAS_SYMBOL_SUFFIX)
 
 #ifdef HAVE_BLAS_ILP64
 #define CBLAS_INT npy_int64
diff --git a/numpy/meson.build b/numpy/meson.build
index 98f40248de51..75d513d176e1 100644
--- a/numpy/meson.build
+++ b/numpy/meson.build
@@ -48,23 +48,18 @@ else
   ]
 endif
 
-macOS13_3_or_later = false
-if host_machine.system() == 'darwin'
-  r = run_command('xcrun', '-sdk', 'macosx', '--show-sdk-version', check: true)
-  sdkVersion = r.stdout().strip()
-
-  macOS13_3_or_later = sdkVersion.version_compare('>=13.3')
-endif
-
+blas_name = get_option('blas')
+lapack_name = get_option('lapack')
+allow_noblas = get_option('allow-noblas')
 # This is currently injected directly into CFLAGS/CXXFLAGS for wheel builds
 # (see cibuildwheel settings in pyproject.toml), but used by CI jobs already
 blas_symbol_suffix = get_option('blas-symbol-suffix')
 
 use_ilp64 = get_option('use-ilp64')
 if not use_ilp64
+  # TODO: clean this up
   # For now, keep supporting the `NPY_USE_BLAS_ILP64` environment variable too
-  # (same as in setup.py) `false is the default for the CLI flag, so check if
-  # env var was set
+  # `false` is the default for the CLI flag, so check if env var was set
   use_ilp64 = run_command(py,
     [
       '-c',
@@ -74,138 +69,97 @@ if not use_ilp64
   ).stdout().strip() == '1'
 endif
 
+if use_ilp64
+  blas_interface = ['interface: ilp64']
+else
+  blas_interface = ['interface: lp64']
+endif
 
-# TODO: 64-bit (ILP64) BLAS and LAPACK support (e.g., check for more .pc files
-# so we detect `openblas64_.so` directly). Partially supported now, needs more
-# auto-detection.
-#
-# Note that this works as long as BLAS and LAPACK are detected properly via
-# pkg-config. By default we look for OpenBLAS, other libraries can be configured via
-# `meson configure -Dblas=blas -Dlapack=lapack` (example to build with Netlib
-# BLAS and LAPACK).
-# For MKL and for auto-detecting one of multiple libs, we'll need a custom
-# dependency in Meson (like is done for scalapack) - see
-# https://github.com/mesonbuild/meson/issues/2835
-blas_name = get_option('blas')
-lapack_name = get_option('lapack')
+# MKL-specific options
+_threading_opt = get_option('mkl-threading')
+if _threading_opt == 'auto'
+  # Switch default to iomp once conda-forge missing openmp.pc issue is fixed
+  mkl_opts = ['threading: seq']
+else
+  mkl_opts = ['threading: ' + _threading_opt]
+endif
+blas_opts = {'mkl': mkl_opts}
+mkl_version_req = '>=2023.0'  # see gh-24824
+mkl_may_use_sdl = not use_ilp64 and _threading_opt in ['auto', 'iomp']
+
+# Note that we can only use a BLAS which provides a CBLAS interface. So disable
+# BLAS completely if CBLAS is not found.
 
-# pkg-config uses a lower-case name while CMake uses a capitalized name, so try
-# that too to make the fallback detection with CMake work
-if blas_name == 'openblas'
-  # first try scipy-openblas, and if found don't look for cblas or lapack
+# First try scipy-openblas, and if found don't look for cblas or lapack, we
+# know what's inside the scipy-openblas wheels already.
+if blas_name == 'openblas' or blas_name == 'auto'
   blas = dependency('scipy-openblas', required: false)
   if blas.found()
     blas_name = 'scipy-openblas'
-  else
-    if use_ilp64
-      _openblas_names = ['openblas64', 'openblas', 'OpenBLAS']
+  endif
+endif
+if blas_name == 'auto'
+  foreach _name : get_option('blas-order')
+    if _name == 'mkl'
+      blas = dependency('mkl',
+        modules: ['cblas'] + blas_interface + mkl_opts,
+        required: false,  # may be required, but we need to emit a custom error message
+        version: mkl_version_req,
+      )
+      # Insert a second try with MKL, because we may be rejecting older versions
+      # or missing it because no pkg-config installed. If so, we need to retry
+      # with MKL SDL, and drop the version constraint (this always worked).
+      if not blas.found() and mkl_may_use_sdl
+        blas = dependency('mkl', modules: ['cblas', 'sdl: true'], required: false)
+      endif
     else
-      _openblas_names = ['openblas', 'OpenBLAS']
+      if _name == 'flexiblas' and use_ilp64
+        _name = 'flexiblas64'
+      endif
+      blas = dependency(_name, modules: ['cblas'] + blas_interface, required: false)
     endif
-  blas = dependency(_openblas_names, required: false)
-  endif
-elif blas_name.to_lower() == 'accelerate'
-  # macOS 13.3+ has updated interfaces aligned with BLAS/LAPACK 3.9.1.  Use them if available.
-  if macOS13_3_or_later
-    accelerate_compile_args = ['-DACCELERATE_NEW_LAPACK']
-    if(use_ilp64)
-      accelerate_compile_args += '-DACCELERATE_LAPACK_ILP64'
+    if blas.found()
+      break
     endif
-    blas = declare_dependency(
-            compile_args: accelerate_compile_args,
-            dependencies: dependency('Accelerate')
-          )
-  else
-    if(use_ilp64)
-      error('macOS SDK 13.3+ is required for ILP64 support.')
-    endif
-    blas = dependency('Accelerate')
-  endif
+  endforeach
 else
-  blas = dependency(blas_name, required: false)
-endif
-have_blas = blas.found()
-cblas = []
-if have_blas
-  # As noted above, at this point the BLAS_SYMBOL_SUFFIX may be injected into
-  # the CFLAGS directly, so this requires care to use that when it happens:
-  if blas_symbol_suffix != ''
-    probe_args = ['-DBLAS_SYMBOL_SUFFIX=' + blas_symbol_suffix]
-  else
-    probe_args = []
-  endif
-
-  # Netlib BLAS has a separate `libcblas.so` which we use directly in the g77
-  # ABI wrappers, so detect it and error out if we cannot find it. OpenBLAS can
-  # be built without CBLAS too (see gh-23909, done by Arch Linux until
-  # recently)
-  # In the future, this should be done automatically for:
-  #   `dependency('blas', modules: cblas)`
-  # see https://github.com/mesonbuild/meson/pull/10921.
-  have_cblas = false
-  if blas_name.to_lower() == 'accelerate'
-    _cblas_header = '<Accelerate/Accelerate.h>'
-  elif blas_name.to_lower().startswith('mkl')
-    _cblas_header = '<mkl_cblas.h>'
-  else
-    _cblas_header = '<cblas.h>'
-  endif
-  if blas_name == 'scipy-openblas'
-    have_cblas = true
-  elif cc.links(f'''
-      #ifndef BLAS_SYMBOL_SUFFIX
-      #  define BLAS_SYMBOL_SUFFIX
-      #endif
-      #define EXPAND(suffix) cblas_ddot ## suffix
-      #define DDOT(suffix) EXPAND(suffix)
-
-      #include @_cblas_header@
-
-      int main(int argc, const char *argv[])
-      {
-          double a[4] = {1,2,3,4};
-          double b[4] = {5,6,7,8};
-          return DDOT(BLAS_SYMBOL_SUFFIX)(4, a, 1, b, 1) > 10;
-      }
-      ''',
-      dependencies: blas,
-      args: probe_args,
-      name: 'CBLAS',
+  if blas_name == 'mkl'
+    blas = dependency('mkl',
+      modules: ['cblas'] + blas_interface + mkl_opts,
+      required: false,
+      version: mkl_version_req,
     )
-    have_cblas = true
-  else
-    cblas = dependency('cblas', required: false)
-    if cblas.found()
-      have_cblas = true
+    # Same deal as above - try again for MKL
+    if not blas.found() and mkl_may_use_sdl
+      blas = dependency('mkl', modules: ['cblas', 'sdl: true'], required: false)
     endif
+  else
+    blas = dependency(blas_name, modules: ['cblas'] + blas_interface, required: false)
   endif
 endif
 
-# BLAS and LAPACK are dependencies for NumPy. Since NumPy 2.0, by default the
-# build will fail if they are missing; the performance impact is large, so
-# using fallback routines must be explicitly opted into by the user. xref
-# gh-24200 for a discussion on this.
-#
-# Note that we can only use a BLAS which provides a CBLAS interface. So disable
-# BLAS completely if CBLAS is not found.
-allow_noblas = get_option('allow-noblas')
+have_blas = blas.found()
 if have_blas
-  _args_blas = []  # note: used for C and C++ via `blas_dep` below
-  if have_cblas
-    _args_blas += ['-DHAVE_CBLAS']
-  elif not allow_noblas
-    error('No CBLAS interface detected! Install a BLAS library with CBLAS ' + \
-          'support, or use the `allow-noblas` build option (note, this ' + \
-          'may be up to 100x slower for some linear algebra operations).')
-  endif
+  _args_blas = ['-DHAVE_CBLAS']  # note: used for C and C++ via `blas_dep` below
   if use_ilp64
     _args_blas += ['-DHAVE_BLAS_ILP64']
+    if 'openblas' in blas.name()
+      _args_blas += ['-DOPENBLAS_ILP64_NAMING_SCHEME']
+    endif
+  endif
+  if blas_symbol_suffix == 'auto'
+    if blas_name == 'scipy-openblas' and use_ilp64
+      blas_symbol_suffix = '64_'
+    else
+      blas_symbol_suffix = blas.get_variable('symbol_suffix', default_value: '')
+    endif
+    message(f'BLAS symbol suffix: @blas_symbol_suffix@')
   endif
   if blas_symbol_suffix != ''
     _args_blas += ['-DBLAS_SYMBOL_SUFFIX=' + blas_symbol_suffix]
   endif
   blas_dep = declare_dependency(
-    dependencies: [blas, cblas],
+    dependencies: [blas],
     compile_args: _args_blas,
   )
 else
@@ -218,37 +172,33 @@ else
   endif
 endif
 
-if blas_name == 'scipy-openblas'
-  lapack_dep = dependency('scipy-openblas', required: false)
-elif lapack_name == 'openblas'
-  lapack_dep = dependency(['openblas', 'OpenBLAS'], required: false)
-elif lapack_name.to_lower() == 'accelerate'
-  # macOS 13.3+ has updated interfaces aligned with BLAS/LAPACK 3.9.1.  Use them if available.
-  if macOS13_3_or_later
-    accelerate_compile_args = ['-DACCELERATE_NEW_LAPACK']
-    if(use_ilp64)
-      accelerate_compile_args += '-DACCELERATE_LAPACK_ILP64'
-    endif
-    lapack_dep = declare_dependency(
-               compile_args: accelerate_compile_args,
-               dependencies: dependency('Accelerate')
-             )
+if 'mkl' in blas.name() or blas.name() == 'accelerate' or blas_name == 'scipy-openblas'
+  # For these libraries we know that they contain LAPACK, and it's desirable to
+  # use that - no need to run the full detection twice.
+  lapack = blas
+else
+  if lapack_name == 'auto'
+    foreach _name : get_option('lapack-order')
+      lapack = dependency(_name, modules: ['lapack'] + blas_interface, required: false)
+      if lapack.found()
+        break
+      endif
+    endforeach
   else
-    if(use_ilp64)
-      error('macOS SDK 13.3+ is required for ILP64 support.')
-    endif
-    lapack_dep = dependency('Accelerate')
+    lapack = dependency(lapack_name, modules: ['lapack'] + blas_interface, required: false)
   endif
-else
-  lapack_dep = dependency(lapack_name, required: false)
 endif
-have_lapack = lapack_dep.found()
+
+have_lapack = lapack.found()
 if not have_lapack and not allow_noblas
   error('No LAPACK library detected! Install one, or use the ' + \
         '`allow-noblas` build option (note, this may be up to 100x slower ' + \
         'for some linear algebra operations).')
+else
+  lapack_dep = declare_dependency(dependencies: [lapack, blas_dep])
 endif
 
+
 # Copy the main __init__.py|pxd files to the build dir (needed for Cython)
 __init__py = fs.copyfile('__init__.py')
 __init__pxd = fs.copyfile('__init__.pxd')
@@ -395,7 +345,7 @@ conf_data.set('PYTHON_VERSION', py.language_version())
 dependency_map = {
   'LAPACK': lapack_dep,
 }
-if have_blas and have_cblas
+if have_blas
   dependency_map += {'BLAS': blas}
 else
   conf_data.set('BLAS_NAME', blas_name)
@@ -409,13 +359,11 @@ foreach name, dep : dependency_map
   if dep.found()
     conf_data.set(name + '_VERSION', dep.version())
     conf_data.set(name + '_TYPE_NAME', dep.type_name())
-    if dep.type_name() == 'pkgconfig'
-      # CMake detection yields less info, so we need to leave it blank there
-      conf_data.set(name + '_INCLUDEDIR', dep.get_variable('includedir'))
-      conf_data.set(name + '_LIBDIR', dep.get_variable('libdir'))
-      conf_data.set(name + '_OPENBLAS_CONFIG', dep.get_variable('openblas_config'))
-      conf_data.set(name + '_PCFILEDIR', dep.get_variable('pcfiledir'))
-    endif
+    # get_variable() results may be missing for a variety of reasons
+    conf_data.set(name + '_INCLUDEDIR', dep.get_variable('includedir', default_value: 'unknown'))
+    conf_data.set(name + '_LIBDIR', dep.get_variable('libdir', default_value: 'unknown'))
+    conf_data.set(name + '_OPENBLAS_CONFIG', dep.get_variable('openblas_config', default_value: 'unknown'))
+    conf_data.set(name + '_PCFILEDIR', dep.get_variable('pcfiledir', default_value: 'unknown'))
   endif
 endforeach
 
diff --git a/pyproject.toml b/pyproject.toml
index bbc7179922bc..2630f5c4a78b 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -153,6 +153,7 @@ tracker = "https://github.com/numpy/numpy/issues"
 skip = "cp36-* cp37-* cp-38* pp37-* *-manylinux_i686 *_ppc64le *_s390x *-musllinux_aarch64"
 build-verbosity = "3"
 before-build = "bash {project}/tools/wheels/cibw_before_build.sh {project}"
+config-settings = "setup-args=-Duse-ilp64=true setup-args=-Dblas=openblas setup-args=-Dlapack=openblas setup-args=-Dblas-symbol-suffix=64_"
 # meson has a hard dependency on ninja, and we need meson to build
 # c-extensions in tests. There is a ninja PyPI package used in
 # build_requirements.txt for macOS, windows, linux but it cannot be in
@@ -165,7 +166,7 @@ test-command = "bash {project}/tools/wheels/cibw_test_command.sh {project}"
 manylinux-x86_64-image = "manylinux2014"
 manylinux-aarch64-image = "manylinux2014"
 musllinux-x86_64-image = "musllinux_1_1"
-environment = { CFLAGS="-fno-strict-aliasing -DBLAS_SYMBOL_SUFFIX=64_ -DHAVE_BLAS_ILP64", LDFLAGS="-Wl,--strip-debug", CXXFLAGS="-DBLAS_SYMBOL_SUFFIX=64_ -DHAVE_BLAS_ILP64", NPY_USE_BLAS_ILP64="1", RUNNER_OS="Linux"}
+environment = {CFLAGS="-fno-strict-aliasing", LDFLAGS="-Wl,--strip-debug", NPY_USE_BLAS_ILP64="1", RUNNER_OS="Linux"}
 
 [tool.cibuildwheel.macos]
 # For universal2 wheels, we will need to fuse them manually
@@ -175,12 +176,13 @@ environment = { CFLAGS="-fno-strict-aliasing -DBLAS_SYMBOL_SUFFIX=64_ -DHAVE_BLA
 # for more info
 archs = "x86_64 arm64"
 test-skip = "*_universal2:arm64"
-# MACOS linker doesn't support stripping symbols
-environment = {CFLAGS="-fno-strict-aliasing -DBLAS_SYMBOL_SUFFIX=64_ -DHAVE_BLAS_ILP64", CXXFLAGS="-DBLAS_SYMBOL_SUFFIX=64_ -DHAVE_BLAS_ILP64", NPY_USE_BLAS_ILP64="1", CC="clang", CXX = "clang++", RUNNER_OS="macOS"}
+# MACOS linker doesn't support stripping symbols.
+# Note that NPY_USE_BLAS_ILP64 is used in `tools/openblas_support.py`.
+environment = {CFLAGS="-fno-strict-aliasing", CC="clang", CXX = "clang++", NPY_USE_BLAS_ILP64="1", RUNNER_OS="macOS"}
 
 [tool.cibuildwheel.windows]
-environment = {NPY_USE_BLAS_ILP64="1", CFLAGS="-DBLAS_SYMBOL_SUFFIX=64_ -DHAVE_BLAS_ILP64", CXXFLAGS="-DBLAS_SYMBOL_SUFFIX=64_ -DHAVE_BLAS_ILP64", LDFLAGS="", PKG_CONFIG_PATH="C:/opt/64/lib/pkgconfig"}
-config-settings = "setup-args=--vsenv"
+environment = {NPY_USE_BLAS_ILP64="1", PKG_CONFIG_PATH="C:/opt/64/lib/pkgconfig"}
+config-settings = "setup-args=--vsenv setup-args=-Duse-ilp64=true setup-args=-Dblas=openblas setup-args=-Dlapack=openblas"
 repair-wheel-command = "bash ./tools/wheels/repair_windows.sh {wheel} {dest_dir}"
 
 [[tool.cibuildwheel.overrides]]
diff --git a/tools/ci/_blis_debian.pc b/tools/ci/_blis_debian.pc
new file mode 100644
index 000000000000..b849b50f6b1f
--- /dev/null
+++ b/tools/ci/_blis_debian.pc
@@ -0,0 +1,8 @@
+libdir=/usr/lib/x86_64-linux-gnu/blis-pthread/
+includedir=/usr/include/x86_64-linux-gnu/blis-pthread
+
+Name: BLIS
+Description: BLAS-like Library Instantiation Software Framework - specific to NumPy CI job, needed until Debian ships blis.pc (see .github/workflows/linux_blas.yml)
+Version: 0.9.0-numpy-ci
+Libs: -L${libdir} -lblis
+Cflags: -I${includedir}
diff --git a/vendored-meson/meson b/vendored-meson/meson
index b7dc7abc4102..66ba7dbbfe28 160000
--- a/vendored-meson/meson
+++ b/vendored-meson/meson
@@ -1 +1 @@
-Subproject commit b7dc7abc4102ec3db4bb9066cb5e674e7a4b08f4
+Subproject commit 66ba7dbbfe2838983f65ad8fe16da1535ebf5b9d