  In this paper, we conjecture an extension to Bressoud's 1996 generalization
of Borwein's famous 1990 conjecture. We then state a few infinite hierarchies
of non-negative $q$-series identities which are interesting examples of our
proposed conjecture and Bressoud's generalized conjecture. Finally, using
certain positivity-preserving transformations for $q$-binomial coefficients, we
prove the non-negativity of the infinite families.
