diff --git a/plum/dispatcher.py b/plum/dispatcher.py
index afd7f35..89bde09 100644
--- a/plum/dispatcher.py
+++ b/plum/dispatcher.py
@@ -1,7 +1,9 @@
 import sys
-from dataclasses import dataclass, field
+from abc import ABCMeta, abstractmethod
+from dataclasses import dataclass, field, replace
 from functools import partial
-from typing import Any, Dict, Optional, Tuple, TypeVar, Union, overload
+from itertools import chain
+from typing import Any, Dict, Optional, Tuple, TypeVar, Union, final, overload
 
 from .function import Function
 from .overload import get_overloads
@@ -19,7 +21,39 @@
 
 
 @dataclass(frozen=True, **_dataclass_kw_args)
-class Dispatcher:
+class AbstractDispatcher(metaclass=ABCMeta):
+    """An abstract dispatcher."""
+
+    @overload
+    def __call__(self, method: T, precedence: int = ...) -> T: ...
+
+    @overload
+    def __call__(self, method: None, precedence: int) -> Callable[[T], T]: ...
+
+    @abstractmethod
+    def __call__(
+        self, method: Optional[T] = None, precedence: int = 0
+    ) -> Union[T, Callable[[T], T]]: ...
+
+    @abstractmethod
+    def abstract(self, method: Callable) -> Function:
+        """Decorator for an abstract function definition. The abstract function
+        definition does not implement any methods."""
+
+    @abstractmethod
+    def multi(
+        self, *signatures: Union[Signature, Tuple[TypeHint, ...]]
+    ) -> Callable[[Callable], Function]:
+        """Decorator to register multiple signatures at once."""
+
+    @abstractmethod
+    def clear_cache(self) -> None:
+        """Clear cache."""
+
+
+@final
+@dataclass(frozen=True, **_dataclass_kw_args)
+class Dispatcher(AbstractDispatcher):
     """A namespace for functions.
 
     Args:
@@ -140,11 +174,160 @@ def _add_method(
             f.register(method, signature, precedence)
         return f
 
-    def clear_cache(self):
+    def clear_cache(self) -> None:
         """Clear cache."""
         for f in self.functions.values():
             f.clear_cache()
 
+    def __or__(self, other: "AbstractDispatcher") -> "DispatcherBundle":
+        if not isinstance(other, AbstractDispatcher):
+            raise ValueError(f"Cannot combine `Dispatcher` with `{type(other)}`.")
+        return DispatcherBundle.from_dispatchers(self, other)
+
+
+@final
+@dataclass(frozen=True, **_dataclass_kw_args)
+class DispatcherBundle(AbstractDispatcher):
+    """A bundle of dispatchers.
+
+    Examples
+    --------
+    >>> from plum import Dispatcher, DispatcherBundle
+
+    >>> dispatch1 = Dispatcher()
+    >>> dispatch2 = Dispatcher()
+
+    >>> dispatchbundle = dispatch1 | dispatch2
+
+    Some Notes:
+
+    At least one dispatcher must be provided to `DispatcherBundle`.
+
+    >>> try:
+    ...     DispatcherBundle()
+    ... except ValueError as e:
+    ...     print(e)
+    At least one dispatcher must be provided to DispatcherBundle.
+
+
+    A `DispatcherBundle` can be created from a sequence of dispatchers.
+
+    >>> dispatchbundle = DispatcherBundle.from_dispatchers(dispatch1, dispatch2)
+
+    A nested `DispatcherBundle` can be flattened.
+
+    >>> dispatch3 = Dispatcher()
+    >>> dispatchbundle = DispatcherBundle.from_dispatchers(dispatchbundle, dispatch3)
+    >>> dispatchbundle
+    DispatcherBundle(dispatchers=(
+        <DispatcherBundle(dispatchers=(
+            <Dispatcher functions={}, classes={} warn_redefinition=False>,
+            <Dispatcher functions={}, classes={} warn_redefinition=False>))>,
+        <Dispatcher functions={}, classes={} warn_redefinition=False>)
+    )
+
+
+    >>> dispatchbundle = dispatchbundle.flatten()
+    DispatcherBundle(dispatchers=(
+        <Dispatcher functions={}, classes={} warn_redefinition=False>,
+        <Dispatcher functions={}, classes={} warn_redefinition=False>,
+        <Dispatcher functions={}, classes={} warn_redefinition=False>)
+    )
+
+    DispatchBundles can be combined with `|`.
+
+    >>> dispatch4 = Dispatcher()
+    >>> dispatchbundle1 = dispatch1 | dispatch2
+    >>> dispatchbundle2 = dispatch3 | dispatch4
+    >>> dispatchbundle = dispatchbundle1 | dispatchbundle2
+    >>> dispatchbundle
+    DispatcherBundle(dispatchers=(
+        <DispatcherBundle(dispatchers=(
+            <Dispatcher functions={}, classes={} warn_redefinition=False>,
+            <Dispatcher functions={}, classes={} warn_redefinition=False>))>,
+        <DispatcherBundle(dispatchers=(
+            <Dispatcher functions={}, classes={} warn_redefinition=False>,
+            <Dispatcher functions={}, classes={} warn_redefinition=False>))>)
+    )
+
+    """
+
+    dispatchers: Tuple[AbstractDispatcher, ...]
+
+    def __post_init__(self) -> None:
+        if not self.dispatchers:
+            msg = "At least one dispatcher must be provided to DispatcherBundle."
+            raise ValueError(msg)
+
+    @classmethod
+    def from_dispatchers(cls, *dispatchers: AbstractDispatcher) -> "DispatcherBundle":
+        """Create a `DispatcherBundle` from a sequence of dispatchers.
+
+        This also flattens nested `DispatcherBundle`s.
+        """
+
+        return cls(dispatchers).flatten()
+
+    def flatten(self) -> "DispatcherBundle":
+        """Flatten the bundle."""
+
+        def as_seq(x: AbstractDispatcher) -> Tuple[AbstractDispatcher, ...]:
+            return x.dispatchers if isinstance(x, DispatcherBundle) else (x,)
+
+        return replace(
+            self, dispatchers=tuple(chain.from_iterable(map(as_seq, self.dispatchers)))
+        )
+
+    @overload
+    def __call__(self, method: T, precedence: int = ...) -> T: ...
+
+    @overload
+    def __call__(self, method: None, precedence: int) -> Callable[[T], T]: ...
+
+    def __call__(
+        self, method: Optional[T] = None, precedence: int = 0
+    ) -> Union[T, Callable[[T], T]]:
+        for dispatcher in self.dispatchers:
+            f = dispatcher(method, precedence=precedence)
+        return f
+
+    def abstract(self, method: Callable) -> Function:
+        """Decorator for an abstract function definition. The abstract function
+        definition does not implement any methods."""
+        for dispatcher in self.dispatchers:
+            f = dispatcher.abstract(method)
+        return f
+
+    def multi(
+        self, *signatures: Union[Signature, Tuple[TypeHint, ...]]
+    ) -> Callable[[Callable], Function]:
+        """Decorator to register multiple signatures at once.
+
+        Args:
+            *signatures (tuple or :class:`.signature.Signature`): Signatures to
+                register.
+
+        Returns:
+            function: Decorator.
+        """
+
+        def decorator(method: Callable) -> Function:
+            for dispatcher in self.dispatchers:
+                f = dispatcher.multi(*signatures)(method)
+            return f
+
+        return decorator
+
+    def clear_cache(self) -> None:
+        """Clear cache."""
+        for dispatcher in self.dispatchers:
+            dispatcher.clear_cache()
+
+    def __or__(self, other: "AbstractDispatcher") -> "DispatcherBundle":
+        if not isinstance(other, AbstractDispatcher):
+            return NotImplemented
+        return self.from_dispatchers(self, other)
+
 
 def clear_all_cache():
     """Clear all cache, including the cache of subclass checks. This should be called
diff --git a/tests/test_dispatcher.py b/tests/test_dispatcher.py
index 5d861a5..5a5d5df 100644
--- a/tests/test_dispatcher.py
+++ b/tests/test_dispatcher.py
@@ -1,3 +1,6 @@
+from numbers import Number
+from types import SimpleNamespace
+
 import pytest
 
 from plum import Dispatcher
@@ -70,3 +73,38 @@ def f(x):
 
     assert f.__doc__ == "Docs"
     assert f.methods == []
+
+
+def test_multiple_dispatchers_on_same_function():
+    dispatch1 = Dispatcher()
+    dispatch2 = Dispatcher()
+
+    @dispatch1.abstract
+    def f(x: Number, y: Number):
+        return x - 2 * y
+
+    @dispatch2.abstract
+    def f(x: Number, y: Number):
+        return x - y
+
+    @(dispatch2 | dispatch1)
+    def f(x: int, y: float):
+        return x + y
+
+    @dispatch1
+    def f(x: str):
+        return x
+
+    ns1 = SimpleNamespace(f=f)
+
+    @dispatch2
+    def f(x: int):
+        return x
+
+    ns2 = SimpleNamespace(f=f)
+
+    assert ns1.f("a") == "a"
+    assert ns1.f(1, 1.0) == 2.0
+
+    assert ns2.f(1) == 1
+    assert ns2.f(1, 1.0) == 2.0