BTW, I understand that child cards work somewhat like this, but when you're starting from the perspective of drawing a bunch of things on each card and trying to link them together, then child cards don't work, because they all share the parent's background image.
What I'm picturing here is really not so much inheritance as composition. One card is providing some kind of global "this deck is an application" logic / overlay, and the other cards can be literally anything you want.