  Here, we analyse two Dirac fermion species in two spatial dimensions in the
presence of general quartic contact interactions. By employing functional
bosonisation techniques, we demonstrate that depending on the couplings of the
fermion interactions the system can be effectively described by a rich variety
of topologically massive gauge theories. Among these effective theories, we
obtain an extended Chern-Simons theory with higher order derivatives as well as
two coupled Chern-Simons theories. Our formalism allows for a general
description of interacting fermions emerging, for example, at the gapped
boundary of three-dimensional topological crystalline insulators.
