  Andrews and Keith recently produced a general Schmidt type partition theorem
using a novel interpretation of Stockhofe's bijection, which they used to find
new $q$-series identities. This includes an identity for a trivariate 2-colored
partition generating function. In this paper, their Schmidt type theorem is
further generalized akin to how Franklin classically extended Glaisher's
theorem. As a consequence, we obtain a companion to Andrews and Keith's
2-colored identity for overpartitions. These identities appear to be special
cases of a much more general result.
