  We give two general transformations that allows certain quite general basic
hypergeometric multi-sums of arbitrary depth (sums that involve an arbitrary
sequence $\{g(k)\}$), to be reduced to an infinite $q$-product times a single
basic hypergeometric sum. Various applications are given, including summation
formulae for some $q$ orthogonal polynomials, and various multi-sums that are
expressible as infinite products.
