diff --git a/CHANGELOG.md b/CHANGELOG.md
index 9235ef8..818333b 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -4,6 +4,8 @@ All notable changes to this project will be documented in this file.
 The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.1.0/).
 
 ## Unreleased
+### Changed
+* `multidispatch` supports variable keyword arguments
 
 ## [1.11.2](https://pypi.org/project/multimethod/1.11.2/) - 2024-02-27
 ### Fixed
diff --git a/multimethod/__init__.py b/multimethod/__init__.py
index 3092425..132cd2d 100644
--- a/multimethod/__init__.py
+++ b/multimethod/__init__.py
@@ -397,7 +397,7 @@ class multidispatch(multimethod, dict[tuple[type, ...], Callable[..., RETURN]]):
     Allows dispatching on keyword arguments based on the first function signature.
     """
 
-    signature: Optional[inspect.Signature]
+    signatures: dict[tuple, inspect.Signature]
 
     def __new__(cls, func: Callable[..., RETURN]) -> "multidispatch[RETURN]":
         return functools.update_wrapper(dict.__new__(cls), func)  # type: ignore
@@ -405,11 +405,8 @@ def __new__(cls, func: Callable[..., RETURN]) -> "multidispatch[RETURN]":
     def __init__(self, func: Callable[..., RETURN]) -> None:
         self.pending = set()
         self.generics = []
-        try:
-            self.signature = inspect.signature(func)
-        except ValueError:
-            self.signature = None
-        msg = "base implementation will eventually ignore annotations as `singledispatch does`"
+        self.signatures = {}
+        msg = "base implementation will eventually ignore annotations as `singledispatch` does"
         with contextlib.suppress(NameError, AttributeError, TypeError):
             hints = signature.from_hints(func)
             if hints and all(map(issubclass, hints, hints)):
@@ -419,9 +416,20 @@ def __init__(self, func: Callable[..., RETURN]) -> None:
     def __get__(self, instance, owner) -> Callable[..., RETURN]:
         return self if instance is None else types.MethodType(self, instance)  # type: ignore
 
+    def __setitem__(self, types: tuple, func: Callable):
+        super().__setitem__(types, func)
+        with contextlib.suppress(ValueError):
+            signature = inspect.signature(func)
+            self.signatures.setdefault(tuple(signature.parameters), signature)
+
     def __call__(self, *args: Any, **kwargs: Any) -> RETURN:
         """Resolve and dispatch to best method."""
-        params = self.signature.bind(*args, **kwargs).args if (kwargs and self.signature) else args
+        params = args
+        if kwargs:
+            for signature in self.signatures.values():  # pragma: no branch
+                with contextlib.suppress(TypeError):
+                    params = signature.bind(*args, **kwargs).args
+                    break
         func = self.dispatch(*params)
         return func(*args, **kwargs)
 
diff --git a/tests/test_dispatch.py b/tests/test_dispatch.py
index f393220..39dfb27 100644
--- a/tests/test_dispatch.py
+++ b/tests/test_dispatch.py
@@ -114,9 +114,10 @@ def _(arg: int):
 
     @func.register
     def _(arg: int, extra: float):
-        return int
+        return float
 
     assert func(0) is func(arg=0) is int
+    assert func(0, 0.0) is func(arg=0, extra=0.0) is float
     assert multidispatch(bool)(1)