diff --git a/funktools/__init__.py b/funktools/__init__.py
index 7d3b2f3..12fcc41 100644
--- a/funktools/__init__.py
+++ b/funktools/__init__.py
@@ -22,6 +22,9 @@ def __getattr__(attr: str) -> typing.Callable:
     elif attr == "template":
         from ._template import _template
         return _template()
+    elif attr == "template":
+        from ._template import TemplateException
+        return TemplateException
     else:
         raise AttributeError(f"Module 'funktools' has no attribute '{attr}'")
 
@@ -33,6 +36,7 @@ def __getattr__(attr: str) -> typing.Callable:
     'Register',
     'Throttle',
     'template',
+    'TemplateException',
 ]
 
 def __dir__():
diff --git a/funktools/_template.py b/funktools/_template.py
index 5e67d4b..6ffb902 100644
--- a/funktools/_template.py
+++ b/funktools/_template.py
@@ -1,56 +1,184 @@
 import inspect
-from typing import Any, Callable
+import typing
 
-_template_funcs: dict[str, Callable] = {}
 
+class TemplateException(Exception):
+    pass
 
-def _infer_types(func):
-    annotations = inspect.get_annotations(func)
-    args = inspect.getfullargspec(func).args
-    return tuple([annotations[arg] for arg in args])
 
+_template_funcs: dict[str, typing.Callable] = {}
 
-class _TemplateFunctionBase:
-    def __init__(self, func, types):
-        if not isinstance(types, tuple):
-            types = tuple([types])
-        self._funcs = {types: func}
 
-    def __call__(self, *args, **kwargs):
-        types = tuple([type(arg) for arg in args])
-        return self._funcs[types](*args, **kwargs)
+class _FuncArgInfo:
+    def __init__(
+        self,
+        func: typing.Callable,
+        annotations: dict = None,
+        fullargspec: inspect.FullArgSpec = None,
+    ):
+        self._func = func
+        self._annotations = annotations
+        self._fullargspec = fullargspec
+        self._arg2type = None
 
-    def __getitem__(self, types):
-        if not isinstance(types, tuple):
-            types = tuple([types])
-        return self._funcs[tuple(types)]
+    def get_func(self):
+        return self._func
+
+    def annotations(self):
+        if self._annotations is None:
+            self._annotations = inspect.get_annotations(self.get_func())
+
+        return self._annotations
+
+    def fullargspec(self):
+        if self._fullargspec is None:
+            self._fullargspec = inspect.getfullargspec(self.get_func())
+
+        return self._fullargspec
+
+    def is_match(self, *args, **kwargs):
+        matched = set()
+
+        argspec = self.fullargspec()
+        matched_via_default = 0
+        if argspec.kwonlydefaults:
+            matched.update(set(argspec.kwonlydefaults.keys()))
+            matched_via_default = len(matched.difference(set(kwargs.keys())))
+
+        for name, val in zip(argspec.args, args):
+            if want_type := self.annotations().get(name):
+                if not isinstance(val, want_type):
+                    return False
+
+            matched.add(name)
 
-    def __setitem__(self, types, func):
-        if not isinstance(types, tuple):
-            types = (types,)
-        self._funcs[types] = func
+        legal_names = set(argspec.args + argspec.kwonlyargs)
+        for name, val in kwargs.items():
+            if name not in legal_names:
+                return False
 
-    def add(self, func):
-        self[_infer_types(func)] = func
+            if want_type := self.annotations().get(name):
+                if not isinstance(val, want_type):
+                    return False
+
+            matched.add(name)
+
+        if (
+            len(matched)
+            == len(argspec.args) + len(argspec.kwonlyargs)
+            == len(args) + len(kwargs) + matched_via_default
+        ):
+            return True
+
+        return False
 
 
 def _make_typed_template_function(name: str):
     """Create a _TemplateFunctionBase object with type `name`"""
+
+    def __init__(self):
+        self._types2funcs = {}
+        self._func_arg_infos = []
+
+    def __call__(self, *args, **kwargs):
+        for func_arg_info in self._func_arg_infos:
+            if func_arg_info.is_match(*args, **kwargs):
+                return func_arg_info.get_func()(*args, **kwargs)
+        raise TemplateException("Cannot find templated function matching signature")
+
+    __call__.__annotations__ = {}
+
+    def __getitem__(self, types):
+        try:
+            return self._types2funcs[types]
+        except KeyError:
+            raise TemplateException(
+                f"Cannot find templated function with types: {types}"
+            )
+
+    __getitem__.__annotations__ = {}
+
+    def __setitem__(self, types: typing.Type | tuple, func: typing.Callable):
+        self._types2funcs[types] = func
+
+        annotations = self.__class__.__getitem__.__annotations__
+
+        if isinstance(types, tuple):
+            types = typing.Tuple[types]
+
+        annotations["types"] = typing.Union[types, annotations.get("types", types)]
+
+        for param, types in inspect.get_annotations(func).items():
+            annotations[param] = typing.Union[types, annotations.get(param, types)]
+
+        annotations["return"] = typing.Callable
+
+        self._append_func_info(func)
+
+    def add(self, func: typing.Callable):
+        annotations = inspect.get_annotations(func)
+        args_annotated = len(annotations)
+        if "return" in annotations:
+            args_annotated = args_annotated - 1
+
+        types = None
+        argspec = inspect.getfullargspec(func)
+        if args_annotated == len(argspec.args):
+            types = tuple([annotations[arg] for arg in argspec.args])
+
+            if len(types) == 1:
+                types = types[0]
+
+            self[types] = func
+
+        self._append_func_info(func, annotations, argspec)
+
+    def _append_func_info(
+        self,
+        func: typing.Callable,
+        annotations: dict = None,
+        fullargspec: inspect.FullArgSpec = None,
+    ):
+        arg_info = _FuncArgInfo(func, annotations, fullargspec)
+
+        call_annotations = self.__class__.__call__.__annotations__
+        all_args = arg_info.fullargspec().args + arg_info.fullargspec().kwonlyargs
+        for arg in all_args:
+            arg_type = arg_info.annotations().get(arg, typing.Any)
+            call_annotations[arg] = arg_type | call_annotations.get(arg, arg_type)
+
+        self._func_arg_infos.append(arg_info)
+
     TemplateFuncMeta = type(name, (type,), {})
-    return TemplateFuncMeta(name, (_TemplateFunctionBase,), {'__name__': name})
+    return TemplateFuncMeta(
+        name,
+        (),
+        {
+            "__init__": __init__,
+            "__call__": __call__,
+            "__getitem__": __getitem__,
+            "__setitem__": __setitem__,
+            "__name__": name,
+            "__annotations__": {},
+            "add": add,
+            "_append_func_info": _append_func_info,
+        },
+    )()
 
 
 class _template:
     def __call__(self, func):
         name = func.__name__
+
         if template_func := _template_funcs.get(name):
-            template_func[_infer_types(func)] = func
+            template_func.add(func)
             return template_func
 
         typed_template_func = _make_typed_template_function(func.__name__)
-        template_func = typed_template_func(func, _infer_types(func))
-        _template_funcs[name] = template_func
-        return template_func
+        typed_template_func.add(func)
+        _template_funcs[name] = typed_template_func
+
+        return typed_template_func
 
     def __getitem__(self, types):
         def _trampoline(func):
@@ -60,9 +188,8 @@ def _trampoline(func):
                 return template_func
 
             typed_template_func = _make_typed_template_function(func.__name__)
-            template_func = typed_template_func(func, types)
-            _template_funcs[name] = template_func
-            return template_func
+            typed_template_func[types] = func
+            _template_funcs[name] = typed_template_func
+            return typed_template_func
 
         return _trampoline
-
diff --git a/test/test_template.py b/test/test_template.py
index b993b6e..850ebbc 100644
--- a/test/test_template.py
+++ b/test/test_template.py
@@ -1,53 +1,77 @@
 from funktools import template
 
 
-class Foo: pass
-class Bar: pass
-class Baz: pass
-class Qux: pass
-class Fee: pass
+class Foo:
+    pass
+
+
+class Bar:
+    pass
+
+
+class Baz:
+    pass
+
+
+class Qux:
+    pass
+
+
+class Fee:
+    pass
+
 
 @template
 def funk():
     return "empty"
 
+
 @template[Foo]
 def funk():
     return "Foo"
 
+
 @template[Bar]
 def funk():
     return "Bar"
 
+
 @template[Baz]
 def funk(baz: Baz):
     return "Baz"
 
+
 @template[Foo, Bar, Baz]
 def funk(baz: Baz):
     return "Foo, Bar, Baz"
 
+
 @template
 def funk(val: int):
     return "int"
 
+
 def foo_qux():
     return "Qux"
+
+
 funk[Qux] = foo_qux
 
+
 def foo_fee(fee: Fee):
     return "Fee"
+
+
 funk.add(foo_fee)
 
-def test_calls() -> None:
+
+def test_typed_calls() -> None:
     assert funk() == "empty"
     assert funk[()]() == "empty"
     assert funk[Foo]() == "Foo"
     assert funk[Bar]() == "Bar"
     assert funk[Baz](Baz()) == "Baz"
     assert funk(Baz()) == "Baz"
-    # TODO(lpe): Should this one eventually allow
-    # funk[Foo, Bar](Baz()) as an equivalent call?
     assert funk[Foo, Bar, Baz](Baz()) == "Foo, Bar, Baz"
     assert funk[int](31) == "int"
     assert funk(42) == "int"
@@ -55,3 +79,37 @@ def test_calls() -> None:
     assert funk[Fee](Fee()) == "Fee"
     assert funk(Fee()) == "Fee"
 
+
+@template
+def funky(a: int, b) -> str:
+    return f"funky({a}: int, {b})"
+
+
+@template
+def funky(a: int, c: float) -> str:
+    return f"funky({a}: int, {c}: float)"
+
+
+@template
+def funky(a: int, b: float, *, c: str, d: tuple = (1,)) -> str:
+    return f"funky({a}: int, {b}: float, *, {c}: str, {d}: tuple)"
+
+
+def test_arg_calls() -> None:
+    assert funky(1, 2.3) == "funky(1: int, 2.3)"
+    assert funky(1, b=2.3) == "funky(1: int, 2.3)"
+    assert funky(a=1, b=2.3) == "funky(1: int, 2.3)"
+    assert funky(b=2.3, a=1) == "funky(1: int, 2.3)"
+
+    assert funky(1, c=3.4) == "funky(1: int, 3.4: float)"
+    assert funky(a=1, c=3.4) == "funky(1: int, 3.4: float)"
+    assert funky(c=3.4, a=1) == "funky(1: int, 3.4: float)"
+
+    assert (
+        funky(1, 2.3, d=(1, 2), c="abc")
+        == "funky(1: int, 2.3: float, *, abc: str, (1, 2): tuple)"
+    )
+    assert (
+        funky(a=1, b=2.3, c="abc")
+        == "funky(1: int, 2.3: float, *, abc: str, (1,): tuple)"
+    )