  The Mal'tsev product of two varieties of the same similarity type is not in
general a variety, because it can fail to be closed under homomorphic images.
In the previous paper we provided a new sufficient condition for such a product
to be a variety. In this paper we extend that result by weakening the
assumptions regarding the two varieties. We also explore the various special
cases of our new result and provide a number of examples of its application.
