  As the field examines a future muon collider as a possible successor to the
LHC, we must consider how to fully utilize not only the high-energy particle
collisions, but also any lower-energy staging facilities necessary in the R&D
process. An economical and efficient possibility is to use the accelerated muon
beam from either the full experiment or from cooling and acceleration tests in
beam-dump experiments.Beam-dump experiments are complementary to the main
collider as they achieve sensitivity to very small couplings with minimal
instrumentation. We demonstrate the utility of muon beam-dump experiments for
new physics searches at energies from 10 GeV to 5 TeV. We find that, even at
low energies like those accessible at staging or demonstrator facilities, it is
possible to probe new regions of parameter space for a variety of generic BSM
models, including muonphilic, leptophilic, $L_\mu - L_\tau$, and dark photon
scenarios. Such experiments could therefore provide opportunities for discovery
of new physics well before the completion of the full multi-TeV collider.
