  In this work we investigate the existence of relativistic models for dark
matter in the context of bimetric gravity, used here to reproduce the modified
Newtonian dynamics (MOND) at galactic scales. For this purpose we consider two
different species of dark matter particles that separately couple to the two
metrics of bigravity. These two sectors are linked together \textit{via} an
internal $U(1)$ vector field, and some effective composite metric built out of
the two metrics. Among possible models only certain classes of kinetic and
interaction terms are allowed without invoking ghost degrees of freedom. Along
these lines we explore the number of allowed kinetic terms in the theory and
point out the presence of ghosts in a previous model. Finally, we propose a
promising class of ghost-free candidate theories that could provide the MOND
phenomenology at galactic scales while reproducing the standard cold dark
matter (CDM) model at cosmological scales.
