Masking Shapes or textures with another Shape?

We love your Shapes asset, but for our game/app we need to find a way to add a grid-like, or checkerboard pattern inside a polygon shape. The polygon can be adjusted at any point and to any shape while retaining the grid inside.

Is there a way to create that pattern with other shapes, then mask it out to show as the fill of the polygon? Or is therer a way to add a texture inside the polygon? I understand Shapes is not designed to work with textures, but I'm asking while crossing my fingers, so that might help. ;)