It has recently been pointed out that placement delivery arrays (PDAs) are equivalent to strong edge colorings of bipartite graphs. In this paper we consider various methods of combining two or more strong edge colorings of bipartite graphs to obtain new ones, and therefore new PDAs. Combining PDAs in certain ways also gives a framework for obtaining PDAs with more robust and flexible parameters. We investigate how the parameters of certain strong edge colorings change after being combined with others and, after comparing the parameters of the resulting PDAs with those of the initial ones, find that subpacketization levels thusly can often be improved.