  The construction of hypergeometric 2D Toda $\tau$-functions as generating
functions for quantum Hurwitz numbers is extended here to multispecies
families. Both the enumerative geometrical significance of these multispecies
quantum Hurwitz numbers as weighted enumerations of branched coverings of the
Riemann sphere and their combinatorial significance in terms of weighted paths
in the Cayley graph of $S_n$ are derived.
