A muon collider could produce the heavier Standard Model particles with a boost, for example in resonant processes such as μ−μ+→ h or μ−μ → Z. We propose machine configurations that produce the boost (asymmetric beam energies, tilted beams) and estimate how much the luminosity is reduced or perhaps enhanced. The feasibility of the proposed configurations, as well as an estimation of the beam-induced backgrounds and beam energy spread, needs to be evaluated in order to derive more solid conclusions on the physics potential of such boosted collider configurations. If achievable, the boost can provide new interesting observational opportunities. For example it can significantly enhance the sensitivity to long-lived new particles decaying in a far-away detector, such as dark higgses or sterile neutrinos produced in h or Z decays.