When we consider multilayer networks, we typically think about multiplex or interconnected complex networks. There is, however, another category of multilayerty embodied in the form of a multilayer network shell that distinguishes the coexisting scales in the structure of a complex network and how they are interrelated. The multiscale unfolding is generated by applying a geometric renormalization protocol acting on the geometric representation of a complex network in hyperbolic space, which have been shown to sustain network navigability and to reveal the mechanisms that govern network structure. We found that multiscale multilayer shells of real networks, including connectomes of the human brain, show multiscale self-similarity, which is also found in the evolution of some growing real networks, suggesting that evolutionary processes can be modeled by reversing renormalization. Multiscale network shells afford us immediate practical applications, including high-fidelity scaled down and scaled up replicas of real networks and a multiscale navigation protocol in hyperbolic space, which betters performance on single layers.