diff --git a/src/aiohappyeyeballs/_staggered.py b/src/aiohappyeyeballs/_staggered.py
new file mode 100644
index 0000000..b5c6798
--- /dev/null
+++ b/src/aiohappyeyeballs/_staggered.py
@@ -0,0 +1,101 @@
+import asyncio
+import contextlib
+from typing import Awaitable, Callable, Iterable, List, Optional, Tuple, TypeVar
+
+
+class _Done(Exception):
+    pass
+
+
+_T = TypeVar("_T")
+
+
+async def staggered_race(
+    coro_fns: Iterable[Callable[[], Awaitable[_T]]], delay: Optional[float]
+) -> Tuple[Optional[_T], Optional[int], List[Optional[BaseException]]]:
+    """
+    Run coroutines with staggered start times and take the first to finish.
+
+    This method takes an iterable of coroutine functions. The first one is
+    started immediately. From then on, whenever the immediately preceding one
+    fails (raises an exception), or when *delay* seconds has passed, the next
+    coroutine is started. This continues until one of the coroutines complete
+    successfully, in which case all others are cancelled, or until all
+    coroutines fail.
+
+    The coroutines provided should be well-behaved in the following way:
+
+    * They should only ``return`` if completed successfully.
+
+    * They should always raise an exception if they did not complete
+      successfully. In particular, if they handle cancellation, they should
+      probably reraise, like this::
+
+        try:
+            # do work
+        except asyncio.CancelledError:
+            # undo partially completed work
+            raise
+
+    Args:
+        coro_fns: an iterable of coroutine functions, i.e. callables that
+            return a coroutine object when called. Use ``functools.partial`` or
+            lambdas to pass arguments.
+
+        delay: amount of time, in seconds, between starting coroutines. If
+            ``None``, the coroutines will run sequentially.
+
+    Returns:
+        tuple *(winner_result, winner_index, exceptions)* where
+
+        - *winner_result*: the result of the winning coroutine, or ``None``
+          if no coroutines won.
+
+        - *winner_index*: the index of the winning coroutine in
+          ``coro_fns``, or ``None`` if no coroutines won. If the winning
+          coroutine may return None on success, *winner_index* can be used
+          to definitively determine whether any coroutine won.
+
+        - *exceptions*: list of exceptions returned by the coroutines.
+          ``len(exceptions)`` is equal to the number of coroutines actually
+          started, and the order is the same as in ``coro_fns``. The winning
+          coroutine's entry is ``None``.
+
+    """
+    # TODO: when we have aiter() and anext(), allow async iterables in coro_fns.
+    winner_result = None
+    winner_index = None
+    exceptions: List[Optional[BaseException]] = []
+
+    async def run_one_coro(
+        this_index: int,
+        coro_fn: Callable[[], Awaitable[_T]],
+        this_failed: asyncio.Event,
+    ) -> None:
+        try:
+            result = await coro_fn()
+        except (SystemExit, KeyboardInterrupt):
+            raise
+        except BaseException as e:
+            exceptions[this_index] = e
+            this_failed.set()  # Kickstart the next coroutine
+        else:
+            # Store winner's results
+            nonlocal winner_index, winner_result
+            assert winner_index is None  # noqa: S101
+            winner_index = this_index
+            winner_result = result
+            raise _Done
+
+    try:
+        async with asyncio.TaskGroup() as tg:
+            for this_index, coro_fn in enumerate(coro_fns):
+                this_failed = asyncio.Event()
+                exceptions.append(None)
+                tg.create_task(run_one_coro(this_index, coro_fn, this_failed))
+                with contextlib.suppress(TimeoutError):
+                    await asyncio.wait_for(this_failed.wait(), delay)
+    except* _Done:
+        pass
+
+    return winner_result, winner_index, exceptions
diff --git a/src/aiohappyeyeballs/impl.py b/src/aiohappyeyeballs/impl.py
index 39e7672..1017e82 100644
--- a/src/aiohappyeyeballs/impl.py
+++ b/src/aiohappyeyeballs/impl.py
@@ -6,9 +6,9 @@
 import itertools
 import socket
 import sys
-from asyncio import staggered
 from typing import List, Optional, Sequence
 
+from . import staggered
 from .types import AddrInfoType
 
 if sys.version_info < (3, 8, 2):  # noqa: UP036
diff --git a/src/aiohappyeyeballs/staggered.py b/src/aiohappyeyeballs/staggered.py
new file mode 100644
index 0000000..6a8b391
--- /dev/null
+++ b/src/aiohappyeyeballs/staggered.py
@@ -0,0 +1,9 @@
+import sys
+
+if sys.version_info > (3, 11):
+    # https://github.com/python/cpython/issues/124639#issuecomment-2378129834
+    from ._staggered import staggered_race
+else:
+    from asyncio.staggered import staggered_race
+
+__all__ = ["staggered_race"]
diff --git a/tests/test_impl.py b/tests/test_impl.py
index 61d34d7..cf23ee2 100644
--- a/tests/test_impl.py
+++ b/tests/test_impl.py
@@ -1368,6 +1368,88 @@ async def _sock_connect(
     ]
 
 
+@patch_socket
+@pytest.mark.asyncio
+@pytest.mark.xfail(reason="raises RuntimeError: coroutine ignored GeneratorExit")
+async def test_handling_system_exit(
+    m_socket: ModuleType,
+) -> None:
+    """Test handling SystemExit."""
+    mock_socket = mock.MagicMock(
+        family=socket.AF_INET,
+        type=socket.SOCK_STREAM,
+        proto=socket.IPPROTO_TCP,
+        fileno=mock.MagicMock(return_value=1),
+    )
+    create_calls = []
+
+    def _socket(*args, **kw):
+        for attr in kw:
+            setattr(mock_socket, attr, kw[attr])
+        return mock_socket
+
+    async def _sock_connect(
+        sock: socket.socket, address: Tuple[str, int, int, int]
+    ) -> None:
+        create_calls.append(address)
+        raise SystemExit
+
+    m_socket.socket = _socket  # type: ignore
+    ipv6_addr_info = (
+        socket.AF_INET6,
+        socket.SOCK_STREAM,
+        socket.IPPROTO_TCP,
+        "",
+        ("dead:beef::", 80, 0, 0),
+    )
+    ipv6_addr_info_2 = (
+        socket.AF_INET6,
+        socket.SOCK_STREAM,
+        socket.IPPROTO_TCP,
+        "",
+        ("dead:aaaa::", 80, 0, 0),
+    )
+    ipv4_addr_info = (
+        socket.AF_INET,
+        socket.SOCK_STREAM,
+        socket.IPPROTO_TCP,
+        "",
+        ("107.6.106.83", 80),
+    )
+    addr_info = [ipv6_addr_info, ipv6_addr_info_2, ipv4_addr_info]
+    local_addr_infos = [
+        (
+            socket.AF_INET6,
+            socket.SOCK_STREAM,
+            socket.IPPROTO_TCP,
+            "",
+            ("::1", 0, 0, 0),
+        ),
+        (
+            socket.AF_INET,
+            socket.SOCK_STREAM,
+            socket.IPPROTO_TCP,
+            "",
+            ("127.0.0.1", 0),
+        ),
+    ]
+    loop = asyncio.get_running_loop()
+    with pytest.raises(SystemExit), mock.patch.object(
+        loop, "sock_connect", _sock_connect
+    ):
+        await start_connection(
+            addr_info,
+            happy_eyeballs_delay=0.3,
+            interleave=2,
+            local_addr_infos=local_addr_infos,
+        )
+
+    # Stopped after the first call
+    assert create_calls == [
+        ("dead:beef::", 80, 0, 0),
+    ]
+
+
 @pytest.mark.asyncio
 @pytest.mark.skipif(sys.version_info >= (3, 8, 2), reason="requires < python 3.8.2")
 def test_python_38_compat() -> None: