  We propose a method to construct a variety of partition identities at once.
The main application is an all-moduli generalization of some of Andrews'
results in [5]. The novelty is that the method constructs solutions to
functional equations which are satisfied by the generating functions. In
contrast, the conventional approach is to show that a variant of well-known
series satisfies the system of functional equations, thus reconciling two
separate lines of computations.
