Massless spin 2 interacting with massive higher spins in d=3

In this paper we consider massless spin 2 interacting with the massive arbitrary spin fermions in d=3. First of all, we study all possible deformations for the massive fermion unfolded equations in the massless spin 2 background. We find three linearly independent solutions one of which corresponds to the standard gravitational interactions. Then for all three cases we reconstruct appropriate Lagrangian formulation.