diff --git a/bin/generate_schema.py b/bin/generate_schema.py
index 39012cdcc..bf562bd4e 100755
--- a/bin/generate_schema.py
+++ b/bin/generate_schema.py
@@ -243,7 +243,6 @@
 non_global_options = {k: {"$ref": f"#/properties/{k}"} for k in schema["properties"]}
 del non_global_options["build"]
 del non_global_options["skip"]
-del non_global_options["container-engine"]
 del non_global_options["test-skip"]
 
 overrides["items"]["properties"]["select"]["oneOf"] = string_array
@@ -254,6 +253,7 @@
 not_linux = non_global_options.copy()
 
 del not_linux["environment-pass"]
+del not_linux["container-engine"]
 for key in list(not_linux):
     if "linux-" in key:
         del not_linux[key]
diff --git a/cibuildwheel/linux.py b/cibuildwheel/linux.py
index 7b1a85af7..55e61f2d3 100644
--- a/cibuildwheel/linux.py
+++ b/cibuildwheel/linux.py
@@ -11,8 +11,8 @@
 from ._compat.typing import assert_never
 from .architecture import Architecture
 from .logger import log
-from .oci_container import OCIContainer
-from .options import Options
+from .oci_container import OCIContainer, OCIContainerEngineConfig
+from .options import BuildOptions, Options
 from .typing import PathOrStr
 from .util import (
     AlreadyBuiltWheelError,
@@ -44,6 +44,7 @@ def path(self) -> PurePosixPath:
 class BuildStep:
     platform_configs: list[PythonConfiguration]
     platform_tag: str
+    container_engine: OCIContainerEngineConfig
     container_image: str
 
 
@@ -65,8 +66,9 @@ def get_python_configurations(
     ]
 
 
-def container_image_for_python_configuration(config: PythonConfiguration, options: Options) -> str:
-    build_options = options.build_options(config.identifier)
+def container_image_for_python_configuration(
+    config: PythonConfiguration, build_options: BuildOptions
+) -> str:
     # e.g
     # identifier is 'cp310-manylinux_x86_64'
     # platform_tag is 'manylinux_x86_64'
@@ -91,15 +93,18 @@ def get_build_steps(
     Groups PythonConfigurations into BuildSteps. Each BuildStep represents a
     separate container instance.
     """
-    steps = OrderedDict[Tuple[str, str, str], BuildStep]()
+    steps = OrderedDict[Tuple[str, str, str, OCIContainerEngineConfig], BuildStep]()
 
     for config in python_configurations:
         _, platform_tag = config.identifier.split("-", 1)
 
-        before_all = options.build_options(config.identifier).before_all
-        container_image = container_image_for_python_configuration(config, options)
+        build_options = options.build_options(config.identifier)
+
+        before_all = build_options.before_all
+        container_image = container_image_for_python_configuration(config, build_options)
+        container_engine = build_options.container_engine
 
-        step_key = (platform_tag, container_image, before_all)
+        step_key = (platform_tag, container_image, before_all, container_engine)
 
         if step_key in steps:
             steps[step_key].platform_configs.append(config)
@@ -107,6 +112,7 @@ def get_build_steps(
             steps[step_key] = BuildStep(
                 platform_configs=[config],
                 platform_tag=platform_tag,
+                container_engine=container_engine,
                 container_image=container_image,
             )
 
@@ -388,29 +394,6 @@ def build_in_container(
 
 
 def build(options: Options, tmp_path: Path) -> None:  # noqa: ARG001
-    try:
-        # check the container engine is installed
-        subprocess.run(
-            [options.globals.container_engine.name, "--version"],
-            check=True,
-            stdout=subprocess.DEVNULL,
-        )
-    except subprocess.CalledProcessError:
-        print(
-            unwrap(
-                f"""
-                cibuildwheel: {options.globals.container_engine} not found. An
-                OCI exe like Docker or Podman is required to run Linux builds.
-                If you're building on Travis CI, add `services: [docker]` to
-                your .travis.yml. If you're building on Circle CI in Linux,
-                add a `setup_remote_docker` step to your .circleci/config.yml.
-                If you're building on Cirrus CI, use `docker_builder` task.
-                """
-            ),
-            file=sys.stderr,
-        )
-        sys.exit(2)
-
     python_configurations = get_python_configurations(
         options.globals.build_selector, options.globals.architectures
     )
@@ -425,6 +408,29 @@ def build(options: Options, tmp_path: Path) -> None:  # noqa: ARG001
     container_package_dir = container_project_path / abs_package_dir.relative_to(cwd)
 
     for build_step in get_build_steps(options, python_configurations):
+        try:
+            # check the container engine is installed
+            subprocess.run(
+                [build_step.container_engine.name, "--version"],
+                check=True,
+                stdout=subprocess.DEVNULL,
+            )
+        except subprocess.CalledProcessError:
+            print(
+                unwrap(
+                    f"""
+                    cibuildwheel: {build_step.container_engine.name} not found. An
+                    OCI exe like Docker or Podman is required to run Linux builds.
+                    If you're building on Travis CI, add `services: [docker]` to
+                    your .travis.yml. If you're building on Circle CI in Linux,
+                    add a `setup_remote_docker` step to your .circleci/config.yml.
+                    If you're building on Cirrus CI, use `docker_builder` task.
+                    """
+                ),
+                file=sys.stderr,
+            )
+            sys.exit(2)
+
         try:
             ids_to_build = [x.identifier for x in build_step.platform_configs]
             log.step(f"Starting container image {build_step.container_image}...")
@@ -435,7 +441,7 @@ def build(options: Options, tmp_path: Path) -> None:  # noqa: ARG001
                 image=build_step.container_image,
                 enforce_32_bit=build_step.platform_tag.endswith("i686"),
                 cwd=container_project_path,
-                engine=options.globals.container_engine,
+                engine=build_step.container_engine,
             ) as container:
                 build_in_container(
                     options=options,
diff --git a/cibuildwheel/oci_container.py b/cibuildwheel/oci_container.py
index ea21e8a29..0a5fa3250 100644
--- a/cibuildwheel/oci_container.py
+++ b/cibuildwheel/oci_container.py
@@ -11,7 +11,7 @@
 import typing
 import uuid
 from collections.abc import Mapping, Sequence
-from dataclasses import dataclass
+from dataclasses import dataclass, field
 from pathlib import Path, PurePath, PurePosixPath
 from types import TracebackType
 from typing import IO, Dict, Literal
@@ -32,7 +32,7 @@
 @dataclass(frozen=True)
 class OCIContainerEngineConfig:
     name: ContainerEngineName
-    create_args: Sequence[str] = ()
+    create_args: tuple[str, ...] = field(default_factory=tuple)
     disable_host_mount: bool = False
 
     @staticmethod
@@ -58,7 +58,7 @@ def from_config_string(config_string: str) -> OCIContainerEngineConfig:
         )
 
         return OCIContainerEngineConfig(
-            name=name, create_args=create_args, disable_host_mount=disable_host_mount
+            name=name, create_args=tuple(create_args), disable_host_mount=disable_host_mount
         )
 
     def options_summary(self) -> str | dict[str, str]:
diff --git a/cibuildwheel/options.py b/cibuildwheel/options.py
index a69664554..8d445179c 100644
--- a/cibuildwheel/options.py
+++ b/cibuildwheel/options.py
@@ -75,7 +75,6 @@ class GlobalOptions:
     build_selector: BuildSelector
     test_selector: TestSelector
     architectures: set[Architecture]
-    container_engine: OCIContainerEngineConfig
 
 
 @dataclasses.dataclass(frozen=True)
@@ -95,6 +94,7 @@ class BuildOptions:
     build_verbosity: int
     build_frontend: BuildFrontendConfig | None
     config_settings: str
+    container_engine: OCIContainerEngineConfig
 
     @property
     def package_dir(self) -> Path:
@@ -544,25 +544,12 @@ def globals(self) -> GlobalOptions:
         )
         test_selector = TestSelector(skip_config=test_skip)
 
-        container_engine_str = self.reader.get(
-            "container-engine",
-            table_format={"item": "{k}:{v}", "sep": "; ", "quote": shlex.quote},
-        )
-
-        try:
-            container_engine = OCIContainerEngineConfig.from_config_string(container_engine_str)
-        except ValueError as e:
-            msg = f"cibuildwheel: Failed to parse container config. {e}"
-            print(msg, file=sys.stderr)
-            sys.exit(2)
-
         return GlobalOptions(
             package_dir=package_dir,
             output_dir=output_dir,
             build_selector=build_selector,
             test_selector=test_selector,
             architectures=architectures,
-            container_engine=container_engine,
         )
 
     def build_options(self, identifier: str | None) -> BuildOptions:
@@ -642,6 +629,8 @@ def build_options(self, identifier: str | None) -> BuildOptions:
 
             manylinux_images: dict[str, str] = {}
             musllinux_images: dict[str, str] = {}
+            container_engine: OCIContainerEngineConfig | None = None
+
             if self.platform == "linux":
                 all_pinned_container_images = _get_pinned_container_images()
 
@@ -676,6 +665,18 @@ def build_options(self, identifier: str | None) -> BuildOptions:
 
                     musllinux_images[build_platform] = image
 
+            container_engine_str = self.reader.get(
+                "container-engine",
+                table_format={"item": "{k}:{v}", "sep": "; ", "quote": shlex.quote},
+            )
+
+            try:
+                container_engine = OCIContainerEngineConfig.from_config_string(container_engine_str)
+            except ValueError as e:
+                msg = f"cibuildwheel: Failed to parse container config. {e}"
+                print(msg, file=sys.stderr)
+                sys.exit(2)
+
             return BuildOptions(
                 globals=self.globals,
                 test_command=test_command,
@@ -692,6 +693,7 @@ def build_options(self, identifier: str | None) -> BuildOptions:
                 musllinux_images=musllinux_images or None,
                 build_frontend=build_frontend,
                 config_settings=config_settings,
+                container_engine=container_engine,
             )
 
     def check_for_invalid_configuration(self, identifiers: Iterable[str]) -> None:
diff --git a/cibuildwheel/resources/cibuildwheel.schema.json b/cibuildwheel/resources/cibuildwheel.schema.json
index 25cf64baa..2681aca5d 100644
--- a/cibuildwheel/resources/cibuildwheel.schema.json
+++ b/cibuildwheel/resources/cibuildwheel.schema.json
@@ -491,6 +491,9 @@
           "config-settings": {
             "$ref": "#/properties/config-settings"
           },
+          "container-engine": {
+            "$ref": "#/properties/container-engine"
+          },
           "dependency-versions": {
             "$ref": "#/properties/dependency-versions"
           },
@@ -579,6 +582,9 @@
         "config-settings": {
           "$ref": "#/properties/config-settings"
         },
+        "container-engine": {
+          "$ref": "#/properties/container-engine"
+        },
         "environment": {
           "$ref": "#/properties/environment"
         },
diff --git a/unit_test/linux_build_steps_test.py b/unit_test/linux_build_steps_test.py
index 29ee25990..f285abec5 100644
--- a/unit_test/linux_build_steps_test.py
+++ b/unit_test/linux_build_steps_test.py
@@ -5,13 +5,13 @@
 from pprint import pprint
 
 import cibuildwheel.linux
-import cibuildwheel.oci_container
+from cibuildwheel.oci_container import OCIContainerEngineConfig
 from cibuildwheel.options import CommandLineArguments, Options
 
 
 def test_linux_container_split(tmp_path: Path, monkeypatch):
     """
-    Tests splitting linux builds by container image and before_all
+    Tests splitting linux builds by container image, container engine, and before_all
     """
 
     args = CommandLineArguments.defaults()
@@ -28,13 +28,17 @@ def test_linux_container_split(tmp_path: Path, monkeypatch):
                 archs = "x86_64 i686"
 
                 [[tool.cibuildwheel.overrides]]
-                select = "cp{38,39,310}-*"
+                select = "cp{37,38,39,310}-*"
                 manylinux-x86_64-image = "other_container_image"
                 manylinux-i686-image = "other_container_image"
 
                 [[tool.cibuildwheel.overrides]]
                 select = "cp39-*"
                 before-all = "echo 'a cp39-only command'"
+
+                [[tool.cibuildwheel.overrides]]
+                select = "cp310-*"
+                container-engine = "docker; create_args: --privileged"
             """
         )
     )
@@ -55,21 +59,35 @@ def identifiers(step):
     def before_alls(step):
         return [options.build_options(c.identifier).before_all for c in step.platform_configs]
 
+    def container_engines(step):
+        return [options.build_options(c.identifier).container_engine for c in step.platform_configs]
+
     pprint(build_steps)
 
+    default_container_engine = OCIContainerEngineConfig(name="docker")
+
     assert build_steps[0].container_image == "normal_container_image"
     assert identifiers(build_steps[0]) == [
         "cp36-manylinux_x86_64",
-        "cp37-manylinux_x86_64",
         "cp311-manylinux_x86_64",
         "cp312-manylinux_x86_64",
     ]
-    assert before_alls(build_steps[0]) == ["", "", "", ""]
+    assert before_alls(build_steps[0]) == [""] * 3
+    assert container_engines(build_steps[0]) == [default_container_engine] * 3
 
     assert build_steps[1].container_image == "other_container_image"
-    assert identifiers(build_steps[1]) == ["cp38-manylinux_x86_64", "cp310-manylinux_x86_64"]
-    assert before_alls(build_steps[1]) == ["", ""]
+    assert identifiers(build_steps[1]) == ["cp37-manylinux_x86_64", "cp38-manylinux_x86_64"]
+    assert before_alls(build_steps[1]) == [""] * 2
+    assert container_engines(build_steps[1]) == [default_container_engine] * 2
 
     assert build_steps[2].container_image == "other_container_image"
     assert identifiers(build_steps[2]) == ["cp39-manylinux_x86_64"]
     assert before_alls(build_steps[2]) == ["echo 'a cp39-only command'"]
+    assert container_engines(build_steps[2]) == [default_container_engine]
+
+    assert build_steps[3].container_image == "other_container_image"
+    assert identifiers(build_steps[3]) == ["cp310-manylinux_x86_64"]
+    assert before_alls(build_steps[3]) == [""]
+    assert container_engines(build_steps[3]) == [
+        OCIContainerEngineConfig(name="docker", create_args=("--privileged",))
+    ]
diff --git a/unit_test/oci_container_test.py b/unit_test/oci_container_test.py
index 161f8cfab..0ff2d363c 100644
--- a/unit_test/oci_container_test.py
+++ b/unit_test/oci_container_test.py
@@ -340,7 +340,7 @@ def test_create_args_volume(tmp_path: Path, container_engine):
     test_mount_dir.mkdir()
     (test_mount_dir / "test_file.txt").write_text("1234")
     container_engine = OCIContainerEngineConfig(
-        name="docker", create_args=[f"--volume={test_mount_dir}:/test_mount"]
+        name="docker", create_args=(f"--volume={test_mount_dir}:/test_mount",)
     )
 
     with OCIContainer(
@@ -356,37 +356,37 @@ def test_create_args_volume(tmp_path: Path, container_engine):
         (
             "docker",
             "docker",
-            [],
+            (),
         ),
         (
             "docker;create_args:",
             "docker",
-            [],
+            (),
         ),
         (
             "docker;create_args:--abc --def",
             "docker",
-            ["--abc", "--def"],
+            ("--abc", "--def"),
         ),
         (
             "docker; create_args: --abc --def",
             "docker",
-            ["--abc", "--def"],
+            ("--abc", "--def"),
         ),
         (
             "name:docker; create_args: --abc --def",
             "docker",
-            ["--abc", "--def"],
+            ("--abc", "--def"),
         ),
         (
             'docker; create_args: --some-option="value with spaces"',
             "docker",
-            ["--some-option=value with spaces"],
+            ("--some-option=value with spaces",),
         ),
         (
             'docker; create_args: --some-option="value; with; semicolons" --another-option',
             "docker",
-            ["--some-option=value; with; semicolons", "--another-option"],
+            ("--some-option=value; with; semicolons", "--another-option"),
         ),
     ],
 )
diff --git a/unit_test/options_test.py b/unit_test/options_test.py
index cf03f8548..288f95caa 100644
--- a/unit_test/options_test.py
+++ b/unit_test/options_test.py
@@ -206,49 +206,49 @@ def test_toml_environment_quoting(tmp_path: Path, toml_assignment, result_value)
         (
             'container-engine = "podman"',
             "podman",
-            [],
+            (),
             False,
         ),
         (
             'container-engine = {name = "podman"}',
             "podman",
-            [],
+            (),
             False,
         ),
         (
             'container-engine = "docker; create_args: --some-option"',
             "docker",
-            ["--some-option"],
+            ("--some-option",),
             False,
         ),
         (
             'container-engine = {name = "docker", create-args = ["--some-option"]}',
             "docker",
-            ["--some-option"],
+            ("--some-option",),
             False,
         ),
         (
             'container-engine = {name = "docker", create-args = ["--some-option", "value that contains spaces"]}',
             "docker",
-            ["--some-option", "value that contains spaces"],
+            ("--some-option", "value that contains spaces"),
             False,
         ),
         (
             'container-engine = {name = "docker", create-args = ["--some-option", "value;that;contains;semicolons"]}',
             "docker",
-            ["--some-option", "value;that;contains;semicolons"],
+            ("--some-option", "value;that;contains;semicolons"),
             False,
         ),
         (
             'container-engine = {name = "docker", disable-host-mount = true}',
             "docker",
-            [],
+            (),
             True,
         ),
         (
             'container-engine = {name = "docker", disable_host_mount = true}',
             "docker",
-            [],
+            (),
             True,
         ),
     ],
@@ -269,7 +269,7 @@ def test_container_engine_option(
     )
 
     options = Options(platform="linux", command_line_arguments=args, env={})
-    parsed_container_engine = options.globals.container_engine
+    parsed_container_engine = options.build_options(None).container_engine
 
     assert parsed_container_engine.name == result_name
     assert parsed_container_engine.create_args == result_create_args
diff --git a/unit_test/validate_schema_test.py b/unit_test/validate_schema_test.py
index 581ac9a7b..698353990 100644
--- a/unit_test/validate_schema_test.py
+++ b/unit_test/validate_schema_test.py
@@ -20,11 +20,39 @@ def test_validate_default_schema():
     assert validator(example) is not None
 
 
-def test_validate_bad_container_engine():
+def test_validate_container_engine():
+    """
+    This test checks container engine can be overridden - it used to be a
+    global option but is now a build option.
+    """
+
     example = tomllib.loads(
         """
+        [tool.cibuildwheel]
+        container-engine = "docker"
+
         [tool.cibuildwheel.linux]
         container-engine = "docker"
+
+        [[tool.cibuildwheel.overrides]]
+        select = "*_x86_64"
+        container-engine = "docker; create_args: --platform linux/arm64/v8"
+        """
+    )
+
+    validator = validate_pyproject.api.Validator()
+    assert validator(example) is not None
+
+
+@pytest.mark.parametrize("platform", ["macos", "windows"])
+def test_validate_bad_container_engine(platform: str):
+    """
+    container-engine is not a valid option for macos or windows
+    """
+    example = tomllib.loads(
+        f"""
+        [tool.cibuildwheel.{platform}]
+        container-engine = "docker"
         """
     )