diff --git a/.github/workflows/publish_pypi.yml b/.github/workflows/publish_pypi.yml
index 4d6d2b65d7..11c4553ead 100644
--- a/.github/workflows/publish_pypi.yml
+++ b/.github/workflows/publish_pypi.yml
@@ -22,6 +22,8 @@ env:
   CIBW_BUILD_VERBOSITY: 2
   # Disable build isolation to allow pre-installing build-time dependencies
   CIBW_BUILD_FRONTEND: "pip; args: --no-build-isolation"
+  CIBW_SKIP: "pp* *musllinux*"
+  FORCE_COLOR: 3
 
 jobs:
   build_windows_wheels:
@@ -72,21 +74,26 @@ jobs:
           if-no-files-found: error
 
   build_macos_and_linux_wheels:
-    name: Build wheels on ${{ matrix.os }}
+    name: Wheels (${{ matrix.os }} / ${{ matrix.arch }})
     runs-on: ${{ matrix.os }}
     strategy:
       fail-fast: false
       matrix:
         os: [ubuntu-latest, macos-latest]
+        arch: [x86_64, aarch64]
+        # build just amd64/x86_64 on macOS until we can get cross-compilation to arm64 working.
+        exclude:
+          - os: macos-latest
+            arch: aarch64
     steps:
       - uses: actions/checkout@v4
         name: Check out PyBaMM repository
 
       - name: Set up QEMU
-        if: matrix.os == 'ubuntu-latest'
+        if: matrix.os == 'ubuntu-latest' && matrix.arch == 'aarch64'
         uses: docker/setup-qemu-action@v3
         with:
-          platforms: all
+          platforms: arm64
 
       - uses: actions/setup-python@v4
         with:
@@ -104,27 +111,47 @@ jobs:
           python -m pip install cmake wget
           python scripts/install_KLU_Sundials.py
 
-      - name: Build wheels on ${{ matrix.os }}
+      - name: Build Linux wheels for ${{ matrix.arch }}
         run: pipx run cibuildwheel --output-dir wheelhouse
+        if: matrix.os == 'ubuntu-latest' && matrix.arch == 'aarch64'
         env:
-          CIBW_ARCHS_LINUX: x86_64 aarch64
+          # on aarch64/arm64, add EPEL to repolist and install openblas-devel from there
+          CIBW_ARCHS_LINUX: aarch64
           CIBW_BEFORE_ALL_LINUX: >
+            yum -y install epel-release &&
             yum -y install openblas-devel lapack-devel &&
             bash scripts/install_sundials.sh 6.0.3 6.5.0
           CIBW_BEFORE_BUILD_LINUX: >
             python -m pip install cmake casadi setuptools wheel
           CIBW_REPAIR_WHEEL_COMMAND_LINUX: >
             auditwheel repair -w {dest_dir} {wheel}
+
+      - name: Build Linux wheels for ${{ matrix.arch }}
+        run: pipx run cibuildwheel --output-dir wheelhouse
+        if: matrix.os == 'ubuntu-latest' && matrix.arch == 'x86_64'
+        env:
+          CIBW_ARCHS_LINUX: x86_64
+          CIBW_BEFORE_ALL_LINUX: >
+            yum -y install openblas-devel lapack-devel &&
+            bash scripts/install_sundials.sh 6.0.3 6.5.0
+          CIBW_BEFORE_BUILD_LINUX: >
+            python -m pip install cmake casadi setuptools wheel
+          CIBW_REPAIR_WHEEL_COMMAND_LINUX: >
+            auditwheel repair -w {dest_dir} {wheel}
+
+      - name: Build macOS wheels for ${{ matrix.arch }}
+        if: matrix.os == 'macos-latest'
+        run: pipx run cibuildwheel --output-dir wheelhouse
+        env:
           CIBW_BEFORE_BUILD_MACOS: >
             python -m pip install --upgrade cmake casadi setuptools wheel && scripts/fix_suitesparse_rpath_mac.sh
           CIBW_REPAIR_WHEEL_COMMAND_MACOS: >
             delocate-listdeps {wheel} && delocate-wheel -v -w {dest_dir} {wheel}
-          CIBW_SKIP: "pp* *musllinux*"
 
       - name: Upload wheels
         uses: actions/upload-artifact@v3
         with:
-          name: wheels
+          name: macos_linux_wheels
           path: ./wheelhouse/*.whl
           if-no-files-found: error
 
@@ -152,7 +179,7 @@ jobs:
           if-no-files-found: error
 
   publish_pypi:
-    if: github.event_name != 'schedule'
+    if: github.event_name != 'schedule' && inputs.target != ''
     name: Upload package to PyPI
     needs: [build_macos_and_linux_wheels, build_windows_wheels, build_sdist]
     runs-on: ubuntu-latest
@@ -163,7 +190,7 @@ jobs:
       - name: Move all package files to files/
         run: |
           mkdir files
-          mv windows_wheels/* wheels/* sdist/* files/
+          mv windows_wheels/* macos_linux_wheels/* sdist/* files/
 
       - name: Publish on PyPI
         if: github.event.inputs.target == 'pypi' || github.event_name == 'release'