We summarize the current state of a concept for muon acceleration aimed at a future Neutrino Factory. The main thrust of these studies was to reduce the overall cost while maintaining performance by exploring the interplay between the complexity of the cooling systems and the acceptance of the accelerator complex. To ensure adequate survival for the short-lived muons, acceleration must occur at high average gradient. The need for large transverse and longitudinal acceptances drives the design of the acceleration system to an initially low RF frequency, e.g., 325 MHz, which is then increased to 650 MHz as the transverse size shrinks with increasing energy. High-gradient normal conducting RF cavities at these frequencies require extremely high peak-power RF sources. Hence superconducting RF (SRF) cavities are chosen. We consider two cost effective schemes for accelerating muon beams for a stageable Neutrino Factory: exploration of the so-called "dual-use" linac concept, where the same linac structure is used for acceleration of both H- and muons and, alternatively, an SRF-efficient design based on a multi-pass (4.5) "dogbone" RLA, extendable to multi-pass FFAG-like arcs.