Let say I have 3 shapes in illustrator: A, B and C. I would like A to overlap B, B to overlap C and C to overlap A. How can I do that?
You have to “cheat”. If it’s a simple enough object, I would just duplicate shape C, bring it to the top, and use a Clipping Mask to cover up everything but the intersection.
To do so, create a shape with no fill or stroke around the intersection (can be any shape but I’m using a rectangle for demonstration):
Select both your empty shape and the duplicated object that should overlap and do Object → Clipping Mask → Make