Hierarchies in NP (under the assumption that P != NP)
Yes! In fact, there is provably an infinite hierarchy of increasingly harder problems between P and NP-complete under the assumption that P!=NP. This is a direct corollary of the proof of Ladner's Theorem (which established the non-emptiness of NP\P)

Formally, we know that for every set S not in P, there exists S' not in P such that S' is Karp-reducible to S but S is not Cook-reducible to S'. Therefore, if P != NP, then there exists an infinite sequence of sets S1, S2... in NP\P such that Si+1 is Karp-reducible to Si but Si is not Cook-reducible to Si+1.

Admittedly, the overwhelming majority of such problems are highly unnatural in nature.