diff --git a/tools/generate_schema_wrapper.py b/tools/generate_schema_wrapper.py
index e7307078a..1dcfd7d45 100644
--- a/tools/generate_schema_wrapper.py
+++ b/tools/generate_schema_wrapper.py
@@ -12,7 +12,7 @@
 from itertools import chain
 from operator import attrgetter
 from pathlib import Path
-from typing import TYPE_CHECKING, Any, Final, Literal
+from typing import TYPE_CHECKING, Any, Final, Generic, Literal, TypedDict, TypeVar
 from urllib import request
 
 import vl_convert as vlc
@@ -317,6 +317,18 @@ def encode(self, *args: Any, {method_args}) -> Self:
         return copy
 '''
 
+# Enables use of ~, &, | with compositions of selection objects.
+DUNDER_PREDICATE_COMPOSITION = """
+    def __invert__(self) -> PredicateComposition:
+        return PredicateComposition({"not": self.to_dict()})
+
+    def __and__(self, other: SchemaBase) -> PredicateComposition:
+        return PredicateComposition({"and": [self.to_dict(), other.to_dict()]})
+
+    def __or__(self, other: SchemaBase) -> PredicateComposition:
+        return PredicateComposition({"or": [self.to_dict(), other.to_dict()]})
+"""
+
 
 # NOTE: Not yet reasonable to generalize `TypeAliasType`, `TypeVar`
 # Revisit if this starts to become more common
@@ -431,6 +443,37 @@ class {classname}({basename}):
     )
 
 
+class MethodSchemaGenerator(SchemaGenerator):
+    """Base template w/ an extra slot `{method_code}` after `{init_code}`."""
+
+    schema_class_template = textwrap.dedent(
+        '''
+    class {classname}({basename}):
+        """{docstring}"""
+        _schema = {schema!r}
+
+        {init_code}
+
+        {method_code}
+    '''
+    )
+
+
+SchGen = TypeVar("SchGen", bound=SchemaGenerator)
+
+
+class OverridesItem(TypedDict, Generic[SchGen]):
+    tp: type[SchGen]
+    kwds: dict[str, Any]
+
+
+CORE_OVERRIDES: dict[str, OverridesItem[SchemaGenerator]] = {
+    "PredicateComposition": OverridesItem(
+        tp=MethodSchemaGenerator, kwds={"method_code": DUNDER_PREDICATE_COMPOSITION}
+    )
+}
+
+
 class FieldSchemaGenerator(SchemaGenerator):
     schema_class_template = textwrap.dedent(
         '''
@@ -656,13 +699,20 @@ def generate_vegalite_schema_wrapper(fp: Path, /) -> str:
         defschema = {"$ref": "#/definitions/" + name}
         defschema_repr = {"$ref": "#/definitions/" + name}
         name = get_valid_identifier(name)
-        definitions[name] = SchemaGenerator(
+        if overrides := CORE_OVERRIDES.get(name):
+            tp = overrides["tp"]
+            kwds = overrides["kwds"]
+        else:
+            tp = SchemaGenerator
+            kwds = {}
+        definitions[name] = tp(
             name,
             schema=defschema,
             schemarepr=defschema_repr,
             rootschema=rootschema,
             basename=basename,
             rootschemarepr=CodeSnippet(f"{basename}._rootschema"),
+            **kwds,
         )
     for name, schema in definitions.items():
         graph[name] = []
diff --git a/tools/schemapi/codegen.py b/tools/schemapi/codegen.py
index 47d96dcd7..37d512087 100644
--- a/tools/schemapi/codegen.py
+++ b/tools/schemapi/codegen.py
@@ -260,16 +260,20 @@ def schema_class(self) -> str:
             basename = self.basename
         else:
             basename = ", ".join(self.basename)
+        docstring = self.docstring(indent=4)
+        init_code = self.init_code(indent=4)
+        if type(self).haspropsetters:
+            method_code = self.overload_code(indent=4)
+        else:
+            method_code = self.kwargs.pop("method_code", None)
         return self.schema_class_template.format(
             classname=self.classname,
             basename=basename,
             schema=schemarepr,
             rootschema=rootschemarepr,
-            docstring=self.docstring(indent=4),
-            init_code=self.init_code(indent=4),
-            method_code=(
-                self.overload_code(indent=4) if type(self).haspropsetters else None
-            ),
+            docstring=docstring,
+            init_code=init_code,
+            method_code=method_code,
             **self.kwargs,
         )