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This paper is a continuation of our previous paper \cite{LOSZ}. For simplecomplex Lie groups with non-trivial center, i.e. classical simply-connectedgroups, $E_6$ and $E_7$ we consider elliptic Modified Calogero-Moser systemscorresponding to the Higgs bundles with an arbitrary characteristic class.These systems are generalization of the classical Calogero-Moser (CM) systemsrelated to a simple Lie groups and contain CM systems related to some(unbroken) subalgebras. For all algebras we construct a special basis,corresponding to non-trivial characteristic classes, the explicit forms of Laxoperators and Hamiltonians.

Characteristic Classes and Integrable Systems for Simple Lie Groups