Don't ever do this. The interaction of different crypto algorithms can be counterintuitive (in the sense that you won't gain what you think you're gaining), it's extraordinarily expensive in ways unbalanced against defenders, and it introduces new implementation errors that can weaken the whole system.

If you're paranoid about AES, use Chapoly (or just use Chapoly because it's in many ways more convenient to use than AES). Don't build elaborate cascades (all cascades qualify), and don't randomize S-boxes.

It is hard enough getting these systems right when you're playing exactly by the book. If you're designing a cryptosystem and you're not a professional cryptographer, the list of things you should be worried about getting wrong is very long and very scary.