The algorithms described in Sections 2.1 through 2.3 can be improved in several ways. For example, by considering the expansion obtained across two or more levels of splitters, it is possible to obtain much larger expansion factors for randomly-wired splitter networks. In fact, it is possible to show that even a splitter network with multiplicity 2 can route any permutation in steps. This is not possible to prove using the previous analysis for splitters with d=2, since they do not have expansion.
One of the nice properties of a d-multibutterfly is that it requires about the same VLSI layout area  as a d-dilated butterfly. In particular, the layout area of an N-input d-butterfly or d-dilated butterfly is . In Section 2.1 we proposed appending a set of levels numbered to the multibutterfly, each isomorphic to the first. Unfortunately, each such level requires area to lay out (as much as the entire multibutterfly), so the total area becomes . For , however, it can be shown that a more area-efficient network will suffice: the multi-Benes network. The multi-Benes network consists of back-to-back multibutterflies and requires twice the area of the multibutterfly.