Cover up (or mask) portion of gameobject(s)

I have a floor GameObject (plane), and I've made a grid of Quads over it (as tiles). Now, the thing is the length of tiles can vary and as such, while placing, it exceeds the dimensions of the floor. So, I was thinking instead of cutting the Quad tile, I'd try and cover it up instead.

'm thinking of a layer system kinda like in Photoshop. So this is what I have in mind:

The smaller squares are the Quad (tiles) and the Red square is the floor (plane). The orange part of the Quad (tiles) shouldn't be visible.

How do I approach this problem? Any help would be appreciated.