diff --git a/.github/workflows/build.yml b/.github/workflows/build.yml
index ec1b9b0c..5e5a8629 100644
--- a/.github/workflows/build.yml
+++ b/.github/workflows/build.yml
@@ -76,8 +76,6 @@ jobs:
     strategy:
       max-parallel: 5
       matrix:
-        # TODO: We should ideally also run this with Windows/Mac clients and a Linux
-        # server. Unsure how to set that up with GitHub Actions though.
         platform: [ubuntu-latest]
         python-version: ['3.8', '3.9', '3.10', '3.11']
 
@@ -98,6 +96,7 @@ jobs:
       # NOTE: Replacing this with our customized version of
       # - uses: koesterlab/setup-slurm-action@v1
       - uses: ./.github/custom_setup_slurm_action
+        timeout-minutes: 5
 
       - name: Test if the slurm cluster is setup correctly
         run: srun --nodes=1 --ntasks=1 --cpus-per-task=1 --mem=1G --time=00:01:00 hostname
@@ -143,43 +142,21 @@ jobs:
           fail_ci_if_error: false
 
   real-slurm-integration-tests:
+
     name: integration tests with a real SLURM cluster
     needs: [mock-slurm-integration-tests]
-    runs-on: self-hosted
 
     strategy:
-      max-parallel: 5
+      max-parallel: 1
       matrix:
         # TODO: We should ideally also run this with Windows/Mac clients and a Linux
         # server. Unsure how to set that up with GitHub Actions though.
-        python-version: ['3.8', '3.9', '3.10', '3.11']
-
-    steps:
-      - uses: actions/checkout@v4
-
-      - name: Set up Python ${{ matrix.python-version }}
-        uses: actions/setup-python@v5
-        with:
-          python-version: ${{ matrix.python-version }}
-
-      - name: Install dependencies
-        run: |
-          python -m pip install --upgrade pip
-          pip install poetry
-          poetry install --with=dev
-
-      - name: Launch integration tests
-        id: self_hosted_integration_tests
-        run: poetry run pytest --slow --cov=milatools --cov-report=xml --cov-append -vvv --log-level=DEBUG
-        timeout-minutes: 30
-        env:
-          SLURM_CLUSTER: mila
-
-      - name: Upload coverage reports to Codecov
-        uses: codecov/codecov-action@v3
-        with:
-          file: ./coverage.xml
-          flags: integrationtests
-          env_vars: PLATFORM,PYTHON
-          name: codecov-umbrella
-          fail_ci_if_error: false
+        python-version: ['3.11']
+        cluster: ['mila']
+    uses: ./.github/workflows/testing.yml
+    with:
+      cluster: ${{ matrix.cluster }}
+      python-version: ${{ matrix.python-version }}
+      timeout-minutes: 30
+    secrets:
+      CODECOV_TOKEN: ${{ secrets.CODECOV_TOKEN }}
diff --git a/.github/workflows/full_cluster_tests.yml b/.github/workflows/full_cluster_tests.yml
new file mode 100644
index 00000000..4db46205
--- /dev/null
+++ b/.github/workflows/full_cluster_tests.yml
@@ -0,0 +1,30 @@
+# Run integration tests on a self-hosted runner using all slurm clusters.
+on:
+  push:
+    branches: "master"  # every time a push is made to `master`, OR
+  schedule:
+    - cron: "30 6 * * 1"  # every Monday at 6:30 AM UTC (2:30 AM Montreal time) OR
+  workflow_dispatch:  # when the workflow is manually triggered
+
+# https://stackoverflow.com/a/72408109/6388696
+# https://docs.github.com/en/actions/using-jobs/using-concurrency#example-using-concurrency-to-cancel-any-in-progress-job-or-run
+concurrency:
+    group: ${{ github.workflow }}-${{ github.ref }}
+    cancel-in-progress: true
+
+jobs:
+  real-slurm-integration-tests:
+    name: integration tests with a real SLURM cluster
+    strategy:
+      max-parallel: 5
+      matrix:
+        # TODO: Setup self-hosted runners inside Mac and Windows VMs.
+        python-version: ['3.11']
+        cluster: ['mila', 'narval', 'beluga', 'cedar', 'graham']
+    uses: ./.github/workflows/testing.yml
+    with:
+      cluster: ${{ matrix.cluster }}
+      python-version: ${{ matrix.python-version }}
+      timeout-minutes: 60
+    secrets:
+      CODECOV_TOKEN: ${{ secrets.CODECOV_TOKEN }}
diff --git a/.github/workflows/testing.yml b/.github/workflows/testing.yml
new file mode 100644
index 00000000..176845ec
--- /dev/null
+++ b/.github/workflows/testing.yml
@@ -0,0 +1,64 @@
+on:
+  workflow_call:
+    inputs:
+      cluster:
+        required: true
+        type: string
+      python-version:
+        required: false
+        type: string
+        default: '3.11'
+      timeout-minutes:
+        required: false
+        type: number
+        default: 30
+    secrets:
+      CODECOV_TOKEN:
+        required: true
+
+  workflow_dispatch:
+
+
+jobs:
+  real-slurm-integration-tests:
+    name: integration tests with a real SLURM cluster
+    runs-on: self-hosted
+
+    steps:
+      - name: Check that we have the pre-existing connection to the SLURM cluster.
+        # TODO: mila cluster doesn't use 2FA yet, so we can actually create the connection
+        # to run the tests; we don't need it to be already running.
+        if: ${{ inputs.cluster != 'mila' && inputs.cluster != 'localhost'}}
+        run:
+            # Check that the control socket is running on the self-hosted runner so
+            # that we don't have to go through 2FA on DRAC clusters.
+            ssh -O check -oStrictHostKeyChecking=no ${{ inputs.cluster }}
+
+      - uses: actions/checkout@v4
+      - name: Set up Python ${{ inputs.python-version }}
+        uses: actions/setup-python@v5
+        with:
+          python-version: ${{ inputs.python-version }}
+
+      - name: Install dependencies
+        run: |
+          python -m pip install --upgrade pip
+          pip install poetry
+          poetry install --with=dev
+
+      - name: Launch integration tests
+        id: self_hosted_integration_tests
+        run: poetry run pytest --slow --cov=milatools --cov-report=xml --cov-append -vvv --log-level=DEBUG
+        timeout-minutes: ${{ inputs.timeout-minutes }}
+        env:
+          SLURM_CLUSTER: ${{ inputs.cluster }}
+
+      - name: Upload coverage reports to Codecov
+        uses: codecov/codecov-action@v3
+        with:
+          token: ${{ secrets.CODECOV_TOKEN }}
+          file: ./coverage.xml
+          flags: integrationtests
+          env_vars: PLATFORM,PYTHON
+          name: codecov-umbrella
+          fail_ci_if_error: false