SU(2|1) supersymmetric multi-particle quantum mechanics with additional semi-dynamical spin degrees of freedom is considered. In particular, we provide an N= 4 supersymmetrization of the quantum U(2) spin Calogero-Moser model, with an intrinsic mass parameter coming from the centrally-extended superalgebra su^ (2 | 1). The full system admits an SU(2|1) covariant separation into the center-of-mass sector and the quotient. We derive explicit expressions for the classical and quantum SU(2|1) generators in both sectors as well as for the total system, and we determine the relevant energy spectra, degeneracies, and the sets of physical states. © 2018, The Author(s).