diff --git a/cibuildwheel/macos.py b/cibuildwheel/macos.py
index 2693f4f3d..20aa3d940 100644
--- a/cibuildwheel/macos.py
+++ b/cibuildwheel/macos.py
@@ -407,7 +407,11 @@ def build(options: Options, tmp_path: Path) -> None:
                                 config.version
                             )
                         )
-                        build_env["PIP_CONSTRAINT"] = constraint_path.as_uri()
+                        user_constraints = build_env.get("PIP_CONSTRAINT")
+                        our_constraints = constraint_path.as_uri()
+                        build_env["PIP_CONSTRAINT"] = " ".join(
+                            c for c in [user_constraints, our_constraints] if c
+                        )
                     build_env["VIRTUALENV_PIP"] = get_pip_version(env)
                     call(
                         "python",
diff --git a/cibuildwheel/windows.py b/cibuildwheel/windows.py
index 3cc92f921..d2be65783 100644
--- a/cibuildwheel/windows.py
+++ b/cibuildwheel/windows.py
@@ -443,7 +443,12 @@ def build(options: Options, tmp_path: Path) -> None:
                             tmp_file.write_bytes(constraints_path.read_bytes())
                             constraints_path = tmp_file
 
-                        build_env["PIP_CONSTRAINT"] = str(constraints_path)
+                        our_constraints = str(constraints_path)
+                        user_constraints = build_env.get("PIP_CONSTRAINT")
+                        build_env["PIP_CONSTRAINT"] = " ".join(
+                            c for c in [our_constraints, user_constraints] if c
+                        )
+
                         build_env["VIRTUALENV_PIP"] = get_pip_version(env)
                         call(
                             "python",
diff --git a/docs/options.md b/docs/options.md
index 427b17e01..e2e742ad1 100644
--- a/docs/options.md
+++ b/docs/options.md
@@ -743,7 +743,7 @@ Platform-specific environment variables are also available:<br/>
     cibuildwheel always defines the environment variable `CIBUILDWHEEL=1`. This can be useful for [building wheels with optional extensions](faq.md#building-packages-with-optional-c-extensions).
 
 !!! note
-    To do its work, cibuildwheel internally sets the options `PIP_CONSTRAINT`, `VIRTUALENV_PIP`, `DIST_EXTRA_CONFIG`, `SETUPTOOLS_EXT_SUFFIX`, `PIP_DISABLE_PIP_VERSION_CHECK`, `PIP_ROOT_USER_ACTION`. Your assignments to these options might be overridden.
+    To do its work, cibuildwheel sets the variables `VIRTUALENV_PIP`, `DIST_EXTRA_CONFIG`, `SETUPTOOLS_EXT_SUFFIX`, `PIP_DISABLE_PIP_VERSION_CHECK`, `PIP_ROOT_USER_ACTION`, and it extends the variables `PATH` and `PIP_CONSTRAINT`. Your assignments to these options might be replaced or extended.
 
 ### `CIBW_ENVIRONMENT_PASS_LINUX` {: #environment-pass}
 > Set environment variables on the host to pass-through to the container.
diff --git a/test/test_environment.py b/test/test_environment.py
index 35de87850..faaba7f3b 100644
--- a/test/test_environment.py
+++ b/test/test_environment.py
@@ -93,3 +93,52 @@ def test_overridden_path(tmp_path, capfd):
     assert len(os.listdir(output_dir)) == 0
     captured = capfd.readouterr()
     assert "python available on PATH doesn't match our installed instance" in captured.err
+
+
+@pytest.mark.parametrize("build_frontend", ["pip", "build"])
+def test_overridden_pip_constraint(tmp_path, build_frontend):
+    """
+    Verify that users can use PIP_CONSTRAINT to specify a specific version of
+    a build-system.requires dependency, by asserting the version of pytz in the
+    setup.py.
+    """
+    project_dir = tmp_path / "project"
+
+    project = test_projects.new_c_project(
+        setup_py_add=textwrap.dedent(
+            """
+            import pytz
+            assert pytz.__version__ == "2022.4"
+        """
+        )
+    )
+    project.files["pyproject.toml"] = textwrap.dedent(
+        """
+        [build-system]
+        requires = ["setuptools", "pytz"]
+        build-backend = "setuptools.build_meta"
+    """
+    )
+    project.generate(project_dir)
+
+    if utils.platform == "linux":
+        # put the constraints file in the project directory, so it's available
+        # in the docker container
+        constraints_file = project_dir / "constraints.txt"
+    else:
+        constraints_file = tmp_path / "constraints.txt"
+
+    constraints_file.write_text("pytz==2022.4")
+
+    actual_wheels = utils.cibuildwheel_run(
+        project_dir,
+        add_env={
+            "CIBW_BUILD": "cp312-*",
+            "CIBW_BUILD_FRONTEND": build_frontend,
+            "PIP_CONSTRAINT": str(constraints_file),
+            "CIBW_ENVIRONMENT_LINUX": "PIP_CONSTRAINT=./constraints.txt",
+        },
+    )
+
+    expected_wheels = [w for w in utils.expected_wheels("spam", "0.1.0") if "cp312" in w]
+    assert set(actual_wheels) == set(expected_wheels)