  We study future coherent elastic neutrino-nucleus scattering (CE$\nu$NS)
modifications from a variety of possible models at the Coherent CAPTAIN Mills
(CCM) experiment at Los Alamos. We show that large regions of Non-Standard
Neutrino Interaction (NSI) parameter space will be excluded rapidly, and that
stringent new bounds on the gauge coupling in $Z'$ models will also be placed.
As a result, CCM will be able to rule out LMA-D solutions for a large class of
models with MeV-scale mediators.
