diff --git a/docs/changelog.md b/docs/changelog.md
index 3f2c1d8e..a168ea10 100644
--- a/docs/changelog.md
+++ b/docs/changelog.md
@@ -2,6 +2,9 @@
 
 ## Unreleased
 
+- Add a mechanism to allow overriding the global variables in an
+  analyzed module. Use this mechanism to set the type of
+  `qcore.testing.Anything` to `Any`. (#786)
 - Rename the `is_compatible` and `get_compatibility_error` functions
   to `is_assignable` and `get_assignability_error` to align with the
   terminology in the typing spec (#785)
diff --git a/pyanalyze/name_check_visitor.py b/pyanalyze/name_check_visitor.py
index 855b14ae..0a9e02d2 100644
--- a/pyanalyze/name_check_visitor.py
+++ b/pyanalyze/name_check_visitor.py
@@ -54,6 +54,7 @@
 import asynq
 import qcore
 import typeshed_client
+from qcore.testing import Anything
 from typing_extensions import Annotated, Protocol, get_args, get_origin
 
 from . import attributes, format_strings, importer, node_visitor, type_evaluation
@@ -627,6 +628,19 @@ def should_check_for_duplicate_values(cls: object, options: Options) -> bool:
     return True
 
 
+def _anything_to_any(obj: object) -> Optional[Value]:
+    if obj is Anything:
+        return AnyValue(AnySource.explicit)
+    return None
+
+
+class TransformGlobals(PyObjectSequenceOption[Callable[[object], Optional[Value]]]):
+    """Transform global variables."""
+
+    name = "transform_globals"
+    default_value = [_anything_to_any]
+
+
 class IgnoredTypesForAttributeChecking(PyObjectSequenceOption[type]):
     """Used in the check for object attributes that are accessed but not set. In general, the check
     will only alert about attributes that don't exist when it has visited all the base classes of
@@ -1181,6 +1195,7 @@ def __init__(
         self.scopes = build_stacked_scopes(
             self.module,
             simplification_limit=self.options.get_value_for(UnionSimplificationLimit),
+            options=self.options,
         )
         self.node_context = StackedContexts()
         self.asynq_checker = AsynqChecker(
@@ -5916,7 +5931,10 @@ def visit_expression(self, node: ast.AST) -> Value:
 
 
 def build_stacked_scopes(
-    module: Optional[types.ModuleType], simplification_limit: Optional[int] = None
+    module: Optional[types.ModuleType],
+    simplification_limit: Optional[int] = None,
+    *,
+    options: Options,
 ) -> StackedScopes:
     # Build a StackedScopes object.
     # Not part of stacked_scopes.py to avoid a circular dependency.
@@ -5928,7 +5946,12 @@ def build_stacked_scopes(
         for key, value in module.__dict__.items():
             val = type_from_annotations(annotations, key, globals=module.__dict__)
             if val is None:
-                val = KnownValue(value)
+                for transformer in options.get_value_for(TransformGlobals):
+                    maybe_val = transformer(value)
+                    if maybe_val is not None:
+                        val = maybe_val
+                if val is None:
+                    val = KnownValue(value)
             module_vars[key] = val
     return StackedScopes(module_vars, module, simplification_limit=simplification_limit)
 
diff --git a/pyanalyze/test_name_check_visitor.py b/pyanalyze/test_name_check_visitor.py
index 60618e65..c74ed2b7 100644
--- a/pyanalyze/test_name_check_visitor.py
+++ b/pyanalyze/test_name_check_visitor.py
@@ -921,6 +921,13 @@ def capybara(foo):
 
             assert_is_value(assert_eq, KnownValue(_assert_eq))
 
+    @assert_passes()
+    def test_transform_globals(self):
+        from qcore.testing import Anything
+
+        def f():
+            assert_is_value(Anything, AnyValue(AnySource.explicit))
+
 
 class TestComprehensions(TestNameCheckVisitorBase):
     @assert_passes()
diff --git a/pyanalyze/test_stacked_scopes.py b/pyanalyze/test_stacked_scopes.py
index 57da5099..f69cf1b4 100644
--- a/pyanalyze/test_stacked_scopes.py
+++ b/pyanalyze/test_stacked_scopes.py
@@ -1,6 +1,7 @@
 # static analysis: ignore
 from .error_code import ErrorCode
 from .name_check_visitor import build_stacked_scopes
+from .options import Options
 from .stacked_scopes import ScopeType, uniq_chain
 from .test_name_check_visitor import TestNameCheckVisitorBase
 from .test_node_visitor import assert_passes, skip_before
@@ -29,7 +30,7 @@ class Module:
 
 class TestStackedScopes:
     def setup_method(self):
-        self.scopes = build_stacked_scopes(Module)
+        self.scopes = build_stacked_scopes(Module, options=Options({}))
 
     def test_scope_type(self):
         assert ScopeType.module_scope == self.scopes.scope_type()