Generalizing Clatworthy Group Divisible Designs II

Clatworthy described the eleven group divisible designs with three groups, block size four, and replication number at most 10. With these in mind one might ask: Can each of these designs be generalized in natural ways? In two previous papers the existence of natural generalizations of four of these designs were settled. Here we essentially settle the existence of natural generalizations of five of the remaining seven Clatworthy designs.