diff --git a/tests/test_type_conversion.py b/tests/test_type_conversion.py
index 83edd1ecb5..40754ba923 100644
--- a/tests/test_type_conversion.py
+++ b/tests/test_type_conversion.py
@@ -146,6 +146,50 @@ def custom_parser(
     assert result.exit_code == 0
 
 
+def test_custom_parse_with_union_type():
+    """parser= should bypass the 'no Union types' assertion."""
+    app = typer.Typer()
+
+    @app.command()
+    def cmd(
+        value: int | str = typer.Argument(
+            None, parser=lambda x: int(x) if x.isdigit() else x
+        ),
+    ):
+        print(repr(value))
+
+    result = runner.invoke(app, ["42"])
+    assert result.exit_code == 0
+    assert "42" in result.output
+
+
+def test_custom_click_type_with_union_type():
+    """click_type= should bypass the 'no Union types' assertion."""
+
+    class FlexType(click.ParamType):
+        name = "flex"
+
+        def convert(
+            self, value: Any, param: click.Parameter | None, ctx: click.Context | None
+        ) -> Any:
+            try:
+                return int(value)
+            except ValueError:
+                return value
+
+    app = typer.Typer()
+
+    @app.command()
+    def cmd(
+        value: int | str = typer.Argument(None, click_type=FlexType()),
+    ):
+        print(repr(value))
+
+    result = runner.invoke(app, ["hello"])
+    assert result.exit_code == 0
+    assert "hello" in result.output
+
+
 def test_custom_click_type():
     class BaseNumberParamType(click.ParamType):
         name = "base_integer"
diff --git a/typer/main.py b/typer/main.py
index 6febf2091e..49771d0ddd 100644
--- a/typer/main.py
+++ b/typer/main.py
@@ -1665,9 +1665,14 @@ def get_click_param(
                 if type_ is NoneType:
                     continue
                 types.append(type_)
-            assert len(types) == 1, "Typer Currently doesn't support Union types"
-            main_type = types[0]
-            origin = get_origin(main_type)
+            if not (
+                parameter_info.parser is not None
+                or parameter_info.click_type is not None
+            ):
+                assert len(types) == 1, "Typer Currently doesn't support Union types"
+            if len(types) == 1:
+                main_type = types[0]
+                origin = get_origin(main_type)
         # Handle Tuples and Lists
         if lenient_issubclass(origin, list):
             main_type = get_args(main_type)[0]