diff --git a/tools/schemapi/vega_expr.py b/tools/schemapi/vega_expr.py
index cf88dc906..8effd0aec 100644
--- a/tools/schemapi/vega_expr.py
+++ b/tools/schemapi/vega_expr.py
@@ -34,13 +34,16 @@
 FUNCTION_DEF_LINE: Pattern[str] = re.compile(r"<a name=\"(.+)\" href=\"#(.+)\">")
 LIQUID_INCLUDE: Pattern[str] = re.compile(r"( \{% include.+%\})")
 
-TYPE: Literal[r"type"] = "type"
+TYPE: Literal[r"type"] = r"type"
 RAW: Literal["raw"] = "raw"
 SOFTBREAK: Literal["softbreak"] = "softbreak"
 TEXT: Literal["text"] = "text"
 CHILDREN: Literal["children"] = "children"
 
 RETURN_ANNOTATION = "FunctionExpression"
+EXPR_ANNOTATION = "IntoExpression"
+NONE: Literal[r"None"] = r"None"
+STAR_ARGS: Literal["*args"] = "*args"
 
 
 def download_expressions_md(url: str, /) -> Path:
@@ -136,14 +139,14 @@ class VegaExprNode:
     parameters: list[VegaExprParam] = dataclasses.field(default_factory=list)
 
     def to_signature(self) -> str:
+        """NOTE: 101/147 cases are all required args."""
         pre_params = f"def {self.name_safe}(cls, "
         post_params = f", /) -> {RETURN_ANNOTATION}:"
         param_list = ""
-        if all(p.required for p in self.parameters):
-            # NOTE: covers 101/147 cases
-            param_list = ", ".join(p.name for p in self.parameters)
+        if self.is_overloaded():
+            param_list = VegaExprParam.star_args()
         else:
-            param_list = "<Not yet handled>"
+            param_list = ", ".join(p.to_str() for p in self.parameters)
         return f"{pre_params}{param_list}{post_params}"
 
     def with_parameters(self) -> Self:
@@ -336,6 +339,19 @@ class VegaExprParam:
     required: bool
     variadic: bool = False
 
+    @staticmethod
+    def star_args() -> LiteralString:
+        return f"{STAR_ARGS}: Any"
+
+    def to_str(self) -> str:
+        """Return as an annotated parameter, with a default if needed."""
+        if self.required:
+            return f"{self.name}: {EXPR_ANNOTATION}"
+        elif not self.variadic:
+            return f"{self.name}: {EXPR_ANNOTATION} = {NONE}"
+        else:
+            return self.star_args()
+
     @classmethod
     def iter_params(cls, raw_texts: Iterable[str], /) -> Iterator[Self]:
         """Yields an ordered parameter list."""
@@ -351,7 +367,7 @@ def iter_params(cls, raw_texts: Iterable[str], /) -> Iterator[Self]:
                 elif s.isalnum():
                     yield cls(s, required=is_required)
                 elif s == "...":
-                    yield cls("*args", required=False, variadic=True)
+                    yield cls(STAR_ARGS, required=False, variadic=True)
                 else:
                     continue