diff --git a/.github/workflows/random_ci_pytest.yml b/.github/workflows/random_ci_pytest.yml
index f50580afc1..11f07100f7 100644
--- a/.github/workflows/random_ci_pytest.yml
+++ b/.github/workflows/random_ci_pytest.yml
@@ -6,31 +6,54 @@ on:
 env:
   PY_COLORS: 1
   PYTEST_ADDOPTS: "--numprocesses=logical"
+  N_RUNS: 5
 
 permissions:
   contents: read
 
 jobs:
+  generate:
+    runs-on: ubuntu-latest
+    outputs:
+      combos: ${{ steps.gen.outputs.combos }}
+    steps:
+      - uses: actions/checkout@de0fac2e4500dabe0009e67214ff5f5447ce83dd # v6.0.2
+      - uses: actions/setup-python@a309ff8b426b58ec0e2a45f0f869d46889d02405 # v6.2.0
+        with:
+          python-version: "3.10"
+      - id: gen
+        name: generate-random-versions
+        run: |
+          python utils/generate_random_versions.py --num "$N_RUNS" --output combos.json
+          echo "combos=$(cat combos.json)" >> "$GITHUB_OUTPUT"
+
   tox:
+    needs: generate
     strategy:
+      fail-fast: false
       matrix:
-        python-version: ["3.10"]
-        os: [ubuntu-latest]
-
-    runs-on: ${{ matrix.os }}
+        combo: ${{ fromJson(needs.generate.outputs.combos) }}
+    runs-on: ubuntu-latest
     steps:
       - uses: actions/checkout@de0fac2e4500dabe0009e67214ff5f5447ce83dd # v6.0.2
       - uses: actions/setup-python@a309ff8b426b58ec0e2a45f0f869d46889d02405 # v6.2.0
         with:
-          python-version: ${{ matrix.python-version }}
+          python-version: "3.10"
       - name: Install uv
         uses: astral-sh/setup-uv@08807647e7069bb48b6ef5acd8ec9567f424441b # v8.1.0
         with:
           enable-cache: "true"
-          cache-suffix: pytest-random-ci-${{ matrix.python-version }}
+          cache-suffix: pytest-random-ci-3.10
           cache-dependency-glob: "pyproject.toml"
-      - name: generate-random-versions
-        run: python utils/generate_random_versions.py
+      - name: write-requirements
+        run: |
+          cat > random-requirements.txt <<EOF
+          pandas==${{ matrix.combo.pandas }}
+          numpy==${{ matrix.combo.numpy }}
+          polars==${{ matrix.combo.polars }}
+          pyarrow==${{ matrix.combo.pyarrow }}
+          EOF
+          cat random-requirements.txt
       - name: install-random-versions
         run: uv pip install -r random-requirements.txt --system
       - name: install-narwhals
diff --git a/utils/generate_random_versions.py b/utils/generate_random_versions.py
index 9c00fca931..8547f3ba17 100644
--- a/utils/generate_random_versions.py
+++ b/utils/generate_random_versions.py
@@ -1,17 +1,19 @@
 from __future__ import annotations
 
+import argparse
+import json
 import random
 from pathlib import Path
 
-PANDAS_AND_NUMPY_VERSION = [
+PANDAS_AND_NUMPY_VERSION = (
     ("1.3.5", "1.21.6"),
     ("1.4.4", "1.22.4"),
     ("1.5.3", "1.23.5"),
     ("2.0.3", "1.24.4"),
     ("2.1.4", "1.25.2"),
     ("2.2.2", "1.26.4"),
-]
-POLARS_VERSION = [
+)
+POLARS_VERSION = (
     "0.20.4",
     "0.20.5",
     "0.20.6",
@@ -35,8 +37,8 @@
     "0.20.31",
     "1.0.0",
     "1.1.0",
-]
-PYARROW_VERSION = [
+)
+PYARROW_VERSION = (
     "13.0.0",
     "14.0.0",
     "14.0.1",
@@ -49,11 +51,68 @@
     "17.0.0",
     "18.0.0",
     "18.1.0",
-]
+)
 
-pandas_version, numpy_version = random.choice(PANDAS_AND_NUMPY_VERSION)
-polars_version = random.choice(POLARS_VERSION)
-pyarrow_version = random.choice(PYARROW_VERSION)
 
-reqs = f"pandas=={pandas_version}\nnumpy=={numpy_version}\npolars=={polars_version}\npyarrow=={pyarrow_version}\n"
-Path("random-requirements.txt").write_text(reqs, "utf-8")
+def sample_distinct(n: int) -> list[dict[str, str]]:
+    """Return `n` combos where no version of any single library is reused."""
+    n_max = min(len(PANDAS_AND_NUMPY_VERSION), len(POLARS_VERSION), len(PYARROW_VERSION))
+    if n > n_max:
+        msg = (
+            f"Requested {n} combos but at most {n_max} are possible "
+            "without reusing a version of any single library."
+        )
+        raise ValueError(msg)
+    pandas_numpy = random.sample(PANDAS_AND_NUMPY_VERSION, n)
+    polars = random.sample(POLARS_VERSION, n)
+    pyarrow = random.sample(PYARROW_VERSION, n)
+    return [
+        {"pandas": pd, "numpy": np, "polars": pl, "pyarrow": pa}
+        for (pd, np), pl, pa in zip(pandas_numpy, polars, pyarrow, strict=True)
+    ]
+
+
+def to_requirements(combo: dict[str, str]) -> str:
+    """Render a single combo as the contents of a requirements.txt file."""
+    return (
+        f"numpy=={combo['numpy']}\n"
+        f"pandas=={combo['pandas']}\n"
+        f"polars=={combo['polars']}\n"
+        f"pyarrow=={combo['pyarrow']}\n"
+    )
+
+
+def main() -> None:
+    """Generate version combos and write them to the requested output path."""
+    parser = argparse.ArgumentParser()
+    parser.add_argument("-n", "--num", type=int, default=1)
+    parser.add_argument(
+        "-o",
+        "--output",
+        type=Path,
+        required=True,
+        help=(
+            "Path to write to. A `.json` extension writes a JSON array of combos; "
+            "any other extension writes a requirements.txt-style file (requires n=1)."
+        ),
+    )
+    args = parser.parse_args()
+
+    num: int = args.num
+    output: Path = args.output
+
+    combos = sample_distinct(n=num)
+
+    if output.suffix == ".json":
+        output.write_text(json.dumps(combos), "utf-8")
+        return
+
+    if num != 1:
+        msg = f"Non-JSON output ({output.suffix or 'no extension'}) requires --num=1"
+        raise ValueError(msg)
+
+    output.write_text(to_requirements(combos[0]), "utf-8")
+
+
+if __name__ == "__main__":
+    main()