diff --git a/libs/langchain/langchain/schema/runnable/base.py b/libs/langchain/langchain/schema/runnable/base.py
index 558495173bc..9b69a9f7114 100644
--- a/libs/langchain/langchain/schema/runnable/base.py
+++ b/libs/langchain/langchain/schema/runnable/base.py
@@ -123,6 +123,7 @@ class Runnable(Generic[Input, Output], ABC):
         other: Union[
             Runnable[Any, Other],
             Callable[[Any], Other],
+            Callable[[Iterator[Any]], Iterator[Other]],
             Mapping[str, Union[Runnable[Any, Other], Callable[[Any], Other], Any]],
         ],
     ) -> RunnableSequence[Input, Other]:
@@ -132,7 +133,8 @@ class Runnable(Generic[Input, Output], ABC):
         self,
         other: Union[
             Runnable[Other, Any],
-            Callable[[Any], Other],
+            Callable[[Other], Any],
+            Callable[[Iterator[Other]], Iterator[Any]],
             Mapping[str, Union[Runnable[Other, Any], Callable[[Other], Any], Any]],
         ],
     ) -> RunnableSequence[Other, Output]:
@@ -353,7 +355,7 @@ class Runnable(Generic[Input, Output], ABC):
             else:
                 # Make a best effort to gather, for any type that supports `+`
                 # This method should throw an error if gathering fails.
-                final += chunk  # type: ignore[operator]
+                final = final + chunk  # type: ignore[operator]
 
         if got_first_val:
             yield from self.stream(final, config, **kwargs)
@@ -379,7 +381,7 @@ class Runnable(Generic[Input, Output], ABC):
             else:
                 # Make a best effort to gather, for any type that supports `+`
                 # This method should throw an error if gathering fails.
-                final += chunk  # type: ignore[operator]
+                final = final + chunk  # type: ignore[operator]
 
         if got_first_val:
             async for output in self.astream(final, config, **kwargs):
@@ -710,7 +712,7 @@ class Runnable(Generic[Input, Output], ABC):
                         final_output = chunk
                     else:
                         try:
-                            final_output += chunk  # type: ignore[operator]
+                            final_output = final_output + chunk  # type: ignore
                         except TypeError:
                             final_output = None
                             final_output_supported = False
@@ -720,7 +722,7 @@ class Runnable(Generic[Input, Output], ABC):
                         final_input = ichunk
                     else:
                         try:
-                            final_input += ichunk  # type: ignore[operator]
+                            final_input = final_input + ichunk  # type: ignore
                         except TypeError:
                             final_input = None
                             final_input_supported = False
@@ -788,7 +790,7 @@ class Runnable(Generic[Input, Output], ABC):
                         final_output = chunk
                     else:
                         try:
-                            final_output += chunk  # type: ignore[operator]
+                            final_output = final_output + chunk  # type: ignore
                         except TypeError:
                             final_output = None
                             final_output_supported = False
@@ -798,7 +800,7 @@ class Runnable(Generic[Input, Output], ABC):
                         final_input = ichunk
                     else:
                         try:
-                            final_input += ichunk  # type: ignore[operator]
+                            final_input = final_input + ichunk  # type: ignore[operator]
                         except TypeError:
                             final_input = None
                             final_input_supported = False
@@ -1315,6 +1317,7 @@ class RunnableSequence(Serializable, Runnable[Input, Output]):
         other: Union[
             Runnable[Any, Other],
             Callable[[Any], Other],
+            Callable[[Iterator[Any]], Iterator[Other]],
             Mapping[str, Union[Runnable[Any, Other], Callable[[Any], Other], Any]],
         ],
     ) -> RunnableSequence[Input, Other]:
@@ -1335,7 +1338,8 @@ class RunnableSequence(Serializable, Runnable[Input, Output]):
         self,
         other: Union[
             Runnable[Other, Any],
-            Callable[[Any], Other],
+            Callable[[Other], Any],
+            Callable[[Iterator[Other]], Iterator[Any]],
             Mapping[str, Union[Runnable[Other, Any], Callable[[Other], Any], Any]],
         ],
     ) -> RunnableSequence[Other, Output]:
@@ -1755,7 +1759,7 @@ class RunnableMapChunk(Dict[str, Any]):
             if key not in chunk or chunk[key] is None:
                 chunk[key] = other[key]
             elif other[key] is not None:
-                chunk[key] += other[key]
+                chunk[key] = chunk[key] + other[key]
         return chunk
 
     def __radd__(self, other: RunnableMapChunk) -> RunnableMapChunk:
@@ -1764,7 +1768,7 @@ class RunnableMapChunk(Dict[str, Any]):
             if key not in chunk or chunk[key] is None:
                 chunk[key] = self[key]
             elif self[key] is not None:
-                chunk[key] += self[key]
+                chunk[key] = chunk[key] + self[key]
         return chunk
 
 
@@ -2107,7 +2111,7 @@ class RunnableGenerator(Runnable[Input, Output]):
             return Any
 
     @property
-    def OutputType(self) -> Type[Output]:
+    def OutputType(self) -> Any:
         func = getattr(self, "_transform", None) or getattr(self, "_atransform")
         try:
             sig = inspect.signature(func)
@@ -2137,7 +2141,7 @@ class RunnableGenerator(Runnable[Input, Output]):
         self,
         input: Iterator[Input],
         config: Optional[RunnableConfig] = None,
-        **kwargs: Any | None,
+        **kwargs: Any,
     ) -> Iterator[Output]:
         return self._transform_stream_with_config(
             input, self._transform, config, **kwargs
@@ -2147,7 +2151,7 @@ class RunnableGenerator(Runnable[Input, Output]):
         self,
         input: Input,
         config: Optional[RunnableConfig] = None,
-        **kwargs: Any | None,
+        **kwargs: Any,
     ) -> Iterator[Output]:
         return self.transform(iter([input]), config, **kwargs)
 
@@ -2159,14 +2163,14 @@ class RunnableGenerator(Runnable[Input, Output]):
             if final is None:
                 final = output
             else:
-                final += output
-        return final
+                final = final + output
+        return cast(Output, final)
 
     def atransform(
         self,
         input: AsyncIterator[Input],
         config: Optional[RunnableConfig] = None,
-        **kwargs: Any | None,
+        **kwargs: Any,
     ) -> AsyncIterator[Output]:
         if not hasattr(self, "_atransform"):
             raise NotImplementedError("This runnable does not support async methods.")
@@ -2179,7 +2183,7 @@ class RunnableGenerator(Runnable[Input, Output]):
         self,
         input: Input,
         config: Optional[RunnableConfig] = None,
-        **kwargs: Any | None,
+        **kwargs: Any,
     ) -> AsyncIterator[Output]:
         async def input_aiter() -> AsyncIterator[Input]:
             yield input
@@ -2187,15 +2191,15 @@ class RunnableGenerator(Runnable[Input, Output]):
         return self.atransform(input_aiter(), config, **kwargs)
 
     async def ainvoke(
-        self, input: Input, config: Optional[RunnableConfig] = None
+        self, input: Input, config: Optional[RunnableConfig] = None, **kwargs: Any
     ) -> Output:
         final = None
-        async for output in self.astream(input, config):
+        async for output in self.astream(input, config, **kwargs):
             if final is None:
                 final = output
             else:
-                final += output
-        return final
+                final = final + output
+        return cast(Output, final)
 
 
 class RunnableLambda(Runnable[Input, Output]):
@@ -2687,7 +2691,7 @@ def coerce_to_runnable(thing: RunnableLike) -> Runnable[Input, Output]:
     elif inspect.isasyncgenfunction(thing) or inspect.isgeneratorfunction(thing):
         return RunnableGenerator(thing)
     elif callable(thing):
-        return RunnableLambda(thing)
+        return RunnableLambda(cast(Callable[[Input], Output], thing))
     elif isinstance(thing, dict):
         runnables: Mapping[str, Runnable[Any, Any]] = {
             key: coerce_to_runnable(r) for key, r in thing.items()
diff --git a/libs/langchain/langchain/schema/runnable/router.py b/libs/langchain/langchain/schema/runnable/router.py
index 6a43e61d69d..f697c0328c9 100644
--- a/libs/langchain/langchain/schema/runnable/router.py
+++ b/libs/langchain/langchain/schema/runnable/router.py
@@ -15,14 +15,7 @@ from typing import (
 from typing_extensions import TypedDict
 
 from langchain.load.serializable import Serializable
-from langchain.schema.runnable.base import (
-    Input,
-    Other,
-    Output,
-    Runnable,
-    RunnableSequence,
-    coerce_to_runnable,
-)
+from langchain.schema.runnable.base import Input, Output, Runnable, coerce_to_runnable
 from langchain.schema.runnable.config import (
     RunnableConfig,
     get_config_list,
@@ -71,28 +64,6 @@ class RouterRunnable(Serializable, Runnable[RouterInput, Output]):
     def get_lc_namespace(cls) -> List[str]:
         return cls.__module__.split(".")[:-1]
 
-    def __or__(
-        self,
-        other: Union[
-            Runnable[Any, Other],
-            Callable[[Any], Other],
-            Mapping[str, Union[Runnable[Any, Other], Callable[[Any], Other]]],
-            Mapping[str, Any],
-        ],
-    ) -> RunnableSequence[RouterInput, Other]:
-        return RunnableSequence(first=self, last=coerce_to_runnable(other))
-
-    def __ror__(
-        self,
-        other: Union[
-            Runnable[Other, Any],
-            Callable[[Any], Other],
-            Mapping[str, Union[Runnable[Other, Any], Callable[[Other], Any]]],
-            Mapping[str, Any],
-        ],
-    ) -> RunnableSequence[Other, Output]:
-        return RunnableSequence(first=coerce_to_runnable(other), last=self)
-
     def invoke(
         self, input: RouterInput, config: Optional[RunnableConfig] = None
     ) -> Output:
diff --git a/libs/langchain/tests/unit_tests/schema/runnable/test_runnable.py b/libs/langchain/tests/unit_tests/schema/runnable/test_runnable.py
index 316a9ecad66..4a63f92ff2a 100644
--- a/libs/langchain/tests/unit_tests/schema/runnable/test_runnable.py
+++ b/libs/langchain/tests/unit_tests/schema/runnable/test_runnable.py
@@ -12,7 +12,6 @@ from typing import (
     cast,
 )
 from uuid import UUID
-from langchain.schema.runnable.base import RunnableGenerator
 
 import pytest
 from freezegun import freeze_time
@@ -57,6 +56,7 @@ from langchain.schema.runnable import (
     RunnableSequence,
     RunnableWithFallbacks,
 )
+from langchain.schema.runnable.base import RunnableGenerator
 from langchain.tools.base import BaseTool, tool
 from langchain.tools.json.tool import JsonListKeysTool, JsonSpec
 
@@ -2876,7 +2876,7 @@ async def test_runnable_gen_transform() -> None:
         async for i in input:
             yield i + 1
 
-    chain = RunnableGenerator(gen_indexes, agen_indexes) | plus_one
+    chain: Runnable = RunnableGenerator(gen_indexes, agen_indexes) | plus_one
     achain = RunnableGenerator(gen_indexes, agen_indexes) | aplus_one
 
     assert chain.input_schema.schema() == {