How to use a different texture on intersecting part of 2 quads

I'm looking for a way to dynamically change a part of a Quad that has a SpriteRenderer attached to it. Let's say I have a red Quad and a blue Quad, and then I drag one onto the other (fast or slow), the intersecting part should be colored using a green sprite. This illustration shows the scenario I'm trying to solve.

A key issue here is that we must use textures/sprites and we have rounded corners, so it's not something we can solve with some maths and dynamically rendered cubes.