diff --git a/mypy/argmap.py b/mypy/argmap.py
index 324ccaf833d5..ff7e94e93cbe 100644
--- a/mypy/argmap.py
+++ b/mypy/argmap.py
@@ -24,6 +24,7 @@ def map_actuals_to_formals(actual_kinds: List[int],
     """
     nformals = len(formal_kinds)
     formal_to_actual = [[] for i in range(nformals)]  # type: List[List[int]]
+    ambiguous_actual_kwargs = []  # type: List[int]
     fi = 0
     for ai, actual_kind in enumerate(actual_kinds):
         if actual_kind == nodes.ARG_POS:
@@ -76,18 +77,25 @@ def map_actuals_to_formals(actual_kinds: List[int],
                         formal_to_actual[formal_kinds.index(nodes.ARG_STAR2)].append(ai)
             else:
                 # We don't exactly know which **kwargs are provided by the
-                # caller. Assume that they will fill the remaining arguments.
-                for fi in range(nformals):
-                    # TODO: If there are also tuple varargs, we might be missing some potential
-                    #       matches if the tuple was short enough to not match everything.
-                    no_certain_match = (
-                        not formal_to_actual[fi]
-                        or actual_kinds[formal_to_actual[fi][0]] == nodes.ARG_STAR)
-                    if ((formal_names[fi]
-                            and no_certain_match
-                            and formal_kinds[fi] != nodes.ARG_STAR) or
-                            formal_kinds[fi] == nodes.ARG_STAR2):
-                        formal_to_actual[fi].append(ai)
+                # caller, so we'll defer until all the other unambiguous
+                # actuals have been processed
+                ambiguous_actual_kwargs.append(ai)
+
+    if ambiguous_actual_kwargs:
+        # Assume the ambiguous kwargs will fill the remaining arguments.
+        #
+        # TODO: If there are also tuple varargs, we might be missing some potential
+        #       matches if the tuple was short enough to not match everything.
+        unmatched_formals = [fi for fi in range(nformals)
+                             if (formal_names[fi]
+                                 and (not formal_to_actual[fi]
+                                      or actual_kinds[formal_to_actual[fi][0]] == nodes.ARG_STAR)
+                                 and formal_kinds[fi] != nodes.ARG_STAR)
+                             or formal_kinds[fi] == nodes.ARG_STAR2]
+        for ai in ambiguous_actual_kwargs:
+            for fi in unmatched_formals:
+                formal_to_actual[fi].append(ai)
+
     return formal_to_actual
 
 
diff --git a/mypy/checkexpr.py b/mypy/checkexpr.py
index 9c0e2f4048b3..fa33161fe4ad 100644
--- a/mypy/checkexpr.py
+++ b/mypy/checkexpr.py
@@ -1336,7 +1336,7 @@ def check_argument_count(self,
                 ok = False
             elif kind in [nodes.ARG_POS, nodes.ARG_OPT,
                           nodes.ARG_NAMED, nodes.ARG_NAMED_OPT] and is_duplicate_mapping(
-                    formal_to_actual[i], actual_kinds):
+                    formal_to_actual[i], actual_types, actual_kinds):
                 if (self.chk.in_checked_function() or
                         isinstance(get_proper_type(actual_types[formal_to_actual[i][0]]),
                                    TupleType)):
@@ -4112,15 +4112,25 @@ def is_non_empty_tuple(t: Type) -> bool:
     return isinstance(t, TupleType) and bool(t.items)
 
 
-def is_duplicate_mapping(mapping: List[int], actual_kinds: List[int]) -> bool:
-    # Multiple actuals can map to the same formal only if they both come from
-    # varargs (*args and **kwargs); in this case at runtime it is possible that
-    # there are no duplicates. We need to allow this, as the convention
-    # f(..., *args, **kwargs) is common enough.
-    return len(mapping) > 1 and not (
-        len(mapping) == 2 and
-        actual_kinds[mapping[0]] == nodes.ARG_STAR and
-        actual_kinds[mapping[1]] == nodes.ARG_STAR2)
+def is_duplicate_mapping(mapping: List[int],
+                         actual_types: List[Type],
+                         actual_kinds: List[int]) -> bool:
+    return (
+        len(mapping) > 1
+        # Multiple actuals can map to the same formal if they both come from
+        # varargs (*args and **kwargs); in this case at runtime it is possible
+        # that here are no duplicates. We need to allow this, as the convention
+        # f(..., *args, **kwargs) is common enough.
+        and not (len(mapping) == 2
+                 and actual_kinds[mapping[0]] == nodes.ARG_STAR
+                 and actual_kinds[mapping[1]] == nodes.ARG_STAR2)
+        # Multiple actuals can map to the same formal if there are multiple
+        # **kwargs which cannot be mapped with certainty (non-TypedDict
+        # **kwargs).
+        and not all(actual_kinds[m] == nodes.ARG_STAR2 and
+                    not isinstance(get_proper_type(actual_types[m]), TypedDictType)
+                    for m in mapping)
+    )
 
 
 def replace_callable_return_type(c: CallableType, new_ret_type: Type) -> CallableType:
diff --git a/test-data/unit/check-kwargs.test b/test-data/unit/check-kwargs.test
index a587be3e06f8..96669e7eea36 100644
--- a/test-data/unit/check-kwargs.test
+++ b/test-data/unit/check-kwargs.test
@@ -377,6 +377,29 @@ f(*l, **d)
 class A: pass
 [builtins fixtures/dict.pyi]
 
+[case testPassingMultipleKeywordVarArgs]
+from typing import Any, Dict
+def f1(a: 'A', b: 'A') -> None: pass
+def f2(a: 'A') -> None: pass
+def f3(a: 'A', **kwargs: 'A') -> None: pass
+def f4(**kwargs: 'A') -> None: pass
+d = None # type: Dict[Any, Any]
+d2 = None # type: Dict[Any, Any]
+f1(**d, **d2)
+f2(**d, **d2)
+f3(**d, **d2)
+f4(**d, **d2)
+class A: pass
+[builtins fixtures/dict.pyi]
+
+[case testPassingKeywordVarArgsToVarArgsOnlyFunction]
+from typing import Any, Dict
+def f(*args: 'A') -> None: pass
+d = None # type: Dict[Any, Any]
+f(**d) # E: Too many arguments for "f"
+class A: pass
+[builtins fixtures/dict.pyi]
+
 [case testKeywordArgumentAndCommentSignature]
 import typing
 def f(x): # type: (int) -> str # N: "f" defined here
diff --git a/test-data/unit/check-python38.test b/test-data/unit/check-python38.test
index 8e013751835f..a115c05bb23e 100644
--- a/test-data/unit/check-python38.test
+++ b/test-data/unit/check-python38.test
@@ -145,11 +145,16 @@ f(arg=1)  # E: Unexpected keyword argument "arg" for "f"
 f(arg="ERROR")  # E: Unexpected keyword argument "arg" for "f"
 
 [case testPEP570Calls]
+from typing import Any, Dict
 def f(p, /, p_or_kw, *, kw) -> None: ...  # N: "f" defined here
+d = None # type: Dict[Any, Any]
 f(0, 0, 0)  # E: Too many positional arguments for "f"
 f(0, 0, kw=0)
 f(0, p_or_kw=0, kw=0)
 f(p=0, p_or_kw=0, kw=0)  # E: Unexpected keyword argument "p" for "f"
+f(0, **d)
+f(**d)  # E: Too few arguments for "f"
+[builtins fixtures/dict.pyi]
 
 [case testPEP570Signatures1]
 def f(p1: bytes, p2: float, /, p_or_kw: int, *, kw: str) -> None:
diff --git a/test-data/unit/check-typeddict.test b/test-data/unit/check-typeddict.test
index 4dc80b1ecd44..2c474f389ad4 100644
--- a/test-data/unit/check-typeddict.test
+++ b/test-data/unit/check-typeddict.test
@@ -1570,6 +1570,24 @@ f1(**c, **a) # E: "f1" gets multiple values for keyword argument "x" \
              # E: Argument "x" to "f1" has incompatible type "str"; expected "int"
 [builtins fixtures/tuple.pyi]
 
+[case testTypedDictAsStarStarAndDictAsStarStar]
+from mypy_extensions import TypedDict
+from typing import Any, Dict
+
+TD = TypedDict('TD', {'x': int, 'y': str})
+
+def f1(x: int, y: str, z: bytes) -> None: ...
+def f2(x: int, y: str) -> None: ...
+
+td: TD
+d = None # type: Dict[Any, Any]
+
+f1(**td, **d)
+f1(**d, **td)
+f2(**td, **d) # E: Too many arguments for "f2"
+f2(**d, **td) # E: Too many arguments for "f2"
+[builtins fixtures/dict.pyi]
+
 [case testTypedDictNonMappingMethods]
 from typing import List
 from mypy_extensions import TypedDict