  We propose a new beam dump experiment at a future TeV-scale muon collider. A
beam dump would be an economical and effective way to increase the discovery
potential of the collider complex in a complementary regime. In this work we
consider vector models such as the dark photon and $L_\mu-L_\tau$ gauge boson
as new physics candidates and explore which novel regions of parameter space
can be probed with a muon beam dump. We find that for the dark photon model, we
gain sensitivity in the moderate mass (MeV - GeV) range at both higher and
lower couplings compared to existing and proposed experiments, and gain access
to previously untouched areas of parameter space of the $L_\mu-L_\tau$ model.
