  We describe the most general ${\rm GL}_{NM}$ classical elliptic
finite-dimensional integrable system, which Lax matrix has $n$ simple poles on
elliptic curve. For $M=1$ it reproduces the classical inhomogeneous spin chain,
for $N=1$ it is the Gaudin type (multispin) extension of the spin
Ruijsenaars-Schneider model, and for $n=1$ the model of $M$ interacting
relativistic ${\rm GL}_N$ tops emerges in some particular case. In this way we
present a classification for relativistic Gaudin models on ${\rm GL}$-bundles
over elliptic curve. As a by-product we describe the inhomogeneous Ruijsenaars
chain. We show that this model can be considered as a particular case of
multispin Ruijsenaars-Schneider model when residues of the Lax matrix are of
rank one. An explicit parametrization of the classical spin variables through
the canonical variables is obtained for this model. Finally, the most general
${\rm GL}_{NM}$ model is also described through $R$-matrices satisfying
associative Yang-Baxter equation. This description provides the trigonometric
and rational analogues of ${\rm GL}_{NM}$ models.
