  Superintegrable systems on a symplectic manifold conventionally are
considered. However, their definition implies a rather restrictive condition
2n=k+m where 2n is a dimension of a symplectic manifold, k is a dimension of a
pointwise Lie algebra of a superintegrable system, and m is its corank. To
solve this problem, we aim to consider partially superintegrable systems on
Poisson manifolds where k+m is the rank of a compatible Poisson structure. The
according extensions of the Mishchenko-Fomenko theorem on generalized
action-angle coordinates is formulated.
