  We make a generalization of the type C monomial space of a single variable,
which was introduced in the construction of type C N-fold supersymmetry, to
several variables. Then, we construct the most general quasi-solvable
second-order operators preserving this multivariate type C space. These
operators of several variables are characterized by the fact that two different
polynomial type solutions are available. In particular, we investigate and
classify all the possible Schroedinger operators realized as a subclass of this
family. It turns out that the rational, hyperbolic, and trigonometric
Calogero-Sutherland models as well as some particular type of the elliptic
Inozemtsev system, all associated with the BC_M root system, fall within the
class.
