Multi-pole extension for elliptic models of interacting integrable tops

We review and give detailed description for ${\mathrm{g}\mathrm{l}}_{NM}$ Gaudin models related to holomorphic vector bundles of rank $NM$ and degree $M$ over elliptic curve with $n$ punctures. Then we introduce their generalizations constructed by means of $R$-matrices satisfying the associative Yang-Baxter equation. A natural extension of the obtained models to the Schlesinger systems is given as well.