  We introduce a family of classical integrable systems describing dynamics of
$M$ interacting ${\rm gl}_N$ integrable tops. It extends the previously known
model of interacting elliptic tops. Our construction is based on the ${\rm
GL}_N$ $R$-matrix satisfying the associative Yang-Baxter equation. The obtained
systems can be considered as extensions of the spin type Calogero-Moser models
with (the classical analogues of) anisotropic spin exchange operators given in
terms of the $R$-matrix data. In $N=1$ case the spin Calogero-Moser model is
reproduced. Explicit expressions for ${\rm gl}_{NM}$-valued Lax pair with
spectral parameter and its classical dynamical $r$-matrix are obtained.
Possible applications are briefly discussed.
