diff --git a/.github/workflows/integration-tests.yml b/.github/workflows/integration-tests.yml
index eccacac588..8cc097a29a 100644
--- a/.github/workflows/integration-tests.yml
+++ b/.github/workflows/integration-tests.yml
@@ -11,24 +11,32 @@ jobs:
       fail-fast: false
       matrix:
         os: [ubuntu-latest]
-        python-version: ["3.8", "3.9", "3.10", "3.11", "pypy-3.8"]
+        python-version: ["3.8", "3.9", "3.10", "3.11"]
     steps:
-      - name: Checkout
-        uses: actions/checkout@v3
-      - name: Base Setup
-        uses: jupyterlab/maintainer-tools/.github/actions/base-setup@v1
+      - uses: actions/checkout@v3
+      - uses: jupyterlab/maintainer-tools/.github/actions/base-setup@v1
       - name: Run the tests
-        run: |
-          hatch run cov:integration
+        run: hatch run cov:integration
       - name: Coverage
         run: |
           pip install codecov coverage[toml]
           codecov
 
+  build_pypy:
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v3
+      - uses: jupyterlab/maintainer-tools/.github/actions/base-setup@v1
+        with:
+          python_version: "pypy-3.8"
+      - name: Run the tests
+        run: hatch run test:nowarn --integration_tests=true
+
   integration_check: # This job does nothing and is only used for the branch protection
     if: always()
     needs:
       - build
+      - build_pypy
     runs-on: ubuntu-latest
     steps:
       - name: Decide whether the needed jobs succeeded or failed
diff --git a/tests/services/contents/test_manager.py b/tests/services/contents/test_manager.py
index ab6960226b..03d51f6770 100644
--- a/tests/services/contents/test_manager.py
+++ b/tests/services/contents/test_manager.py
@@ -163,6 +163,9 @@ def test_get_os_path(jp_file_contents_manager_class, tmp_path):
     fs_path = os.path.join(fm.root_dir, "test.ipynb")
     assert path == fs_path
 
+
+@pytest.mark.skipif(os.name == "nt", reason="Posix only")
+def test_get_os_path_posix(jp_file_contents_manager_class, tmp_path):
     fm = jp_file_contents_manager_class(root_dir=str(tmp_path))
     path = fm._get_os_path("////test.ipynb")
     fs_path = os.path.join(fm.root_dir, "test.ipynb")