Relativistic interacting integrable elliptic tops

We propose a relativistic generalization of integrable systems describing $M$ interacting elliptic $gl(N)$ Euler–Arnold tops. The obtained models are elliptic integrable systems that reproduce the spin elliptic $GL(M)$ Ruijsenaars–Schneider model with $N=1$ and relativistic integrable $GL(N)$ elliptic tops with $M=1$. We construct the Lax pairs with a spectral parameter on the elliptic curve.