I recently learned that one of the many lessons that one can learn from the AdS/CFT correspondence is that there could be two classical limits (the bulk with gravity in $D+1$ spatial dimensions, and the boundary theory with $D$ spatial dimensions without gravity) of a quantum theory, namely the underlying quantum gravity theory. (Reference: This paper by Sean Carroll, Page 3) Here, of course, the ''classical'' limit simply means the low energy limit and does not really mean the classical limit as far as I can understand (i.e., the boundary theory is a CFT--not a classical theory in the sense of a non-quantum theory).
I am curious if there can be more than one classical limits of a simple quantum theory (not a quantum gravity theory but a simple non-relativistic quantum theory) in the basic sense of in which one usually means classical limit (i.e. the $h\to0$ limit).