Is there a non-trivial limit to a number of nested orbits?
There is no theoretical maximum. It would be possible for the solar system to orbit a sufficiently large mass, (while the planets' orbits remain stable). And it would be possible for that large mass to orbit another, even larger mass. The process could, in theory, be repeated without limit. The masses of the central bodies would have to be exponentially larger with each embedding, and so could not be conventional stars, beyond a certain point. (They could be black holes)

This is the absence of theoretical limit imposed by the theory of gravitation. In practice, multiple levels of orbits don't exist, since there does not exist a mechanism that can create the massive central bodies in the right orbits.