Muon-based facilities offer unique potential to provide capabilities at both the Intensity Frontier with Neutrino Factories and the Energy Frontier with Muon Colliders. They rely on a novel technology with challenging parameters, for which the feasibility is currently being evaluated by the Muon Accelerator Program (MAP). A realistic scenario for a complementary series of staged facilities with increasing complexity and significant physics potential at each stage has been developed. It takes advantage of and leverages the capabilities already planned for Fermilab, especially the strategy for long-term improvement of the accelerator complex being initiated with the Proton Improvement Plan (PIP-II) and the Long Baseline Neutrino Facility (LBNF). Each stage is designed to provide an R&D platform to validate the technologies required for subsequent stages. The rationale and sequence of the staging process and the critical issues to be addressed at each stage, are presented.