  A class of multidimensional integrable hierarchies connected with commutation
of general (unreduced) (N+1)-dimensional vector fields containing derivative
over spectral variable is considered. They are represented in the form of
generating equation, as well as in the Lax-Sato form. A dressing scheme based
on nonlinear vector Riemann problem is presented for this class. The
hierarchies connected with Manakov-Santini equation and Dunajski system are
considered as illustrative examples.
