stochastic processes – universality for scale-dependent systems?

Researchers who consider critical points in dynamic systems often think that these systems belong to universality classes, so that the behavior of the system at its critical point depends only on its universal class and not on its exact specification.

From what I have read and seen, I have the impression that universality is just considered relevant at the critical point, since only here is the system scalar-variable.

My question is, What if the large-scale behavior is controlled by another dynamic system so that the entire system is not skalvariant?

I feel that it should still make sense to talk about the behavior of the system as a whole if it is equal among different decisions of small-scale dynamics and gives a form of universality. However, I have not found a discussion about such a thing. I would like to know if the concept makes sense and what a good starting point to think about it.