  We introduce and investigate a family of tau-functions of the 2D Toda
hierarchy, which is a natural generalization of the hypergeometric family
associated with Hurwitz numbers. For this family we prove a skew Schur function
expansion formula. For arbitrary rational weight generating functions we
construct the multi-matrix models. Two different types of cut-and-join
descriptions are derived. Considered examples include generalized fully simple
maps, which we identify with the recently introduced skew hypergeometric
tau-functions.
