Integrable system of generalized relativistic interacting tops

We describe a family of integrable GL(NM) models generalizing classical spin Ruijsenaars-Schneider systems (the case N = 1) on one hand and relativistic integrable tops on the GL(N) Lie group (the case M = 1) on the other hand. We obtain the described models using the Lax pair with a spectral parameter and derive the equations of motion. To construct the Lax representation, we use the GL(N) R-matrix in the fundamental representation of GL(N).