Session types denote message protocols between concurrent processes, allowing a type-safe expression of inter-process communication. Although previous work demonstrate a well-defined notion of subtyping where processes have different perceptions of the protocol, these formulations were limited to linear session types where each channel of communication has a unique provider and client. In this paper, we extend subtyping to shared session types where channels can now have multiple clients instead of a single client. We demonstrate that this generalization can statically capture protocol requirements that span multiple phases of interactions of a client with a shared service provider, something not possible in prior proposals. Moreover, the phases are manifest in the type of the client.