Can I map a 2nd texture onto a sprite that's already mapped with an atlas?

I have a sprite that is made from part of a texture atlas. Is it possible to also map a simple square texture onto it? I want to use the second texture within a custom shader as a mask for colour changes. The colour changes work, but I can't yet map the mask in order to control where they happen.

It would not be efficient to make a mask using the same UVs as the texture atlas as after this I would also like to change the tiling of the mask and re-use it for other sprites.