The diversity in eukaryotic life reflects a diversity in regulatory pathways. Nocedal and Johnson argue that the rewiring of gene regulatory networks is a major force for the diversity of life, that changes in regulation can create new species. We have created a method (based on our new “ping-pong algorithm) for detecting more complicated rewirings, where several transcription factors can substitute for one or more transcription factors in the regulation of a family of co-regulated genes. An example is illustrative. A rewiring has been reported by Hogues et al. that RAP1 in Saccharomyces cerevisiae substitutes for TBF1/CBF1 in Candida albicans for ribosomal RP genes. There one transcription factor substitutes for another on some collection of genes. Such a substitution is referred to as a “rewiring”. We agree with this finding of rewiring as far as it goes but the situation is more complicated. Many transcription factors can regulate a gene and our algorithm finds that in this example a “team” (or collection) of three transcription factors including RAP1 substitutes for TBF1 for 19 genes. The switch occurs for a branch of the phylogenetic tree containing 10 species (including Saccharomyces cerevisiae), while the remaining 13 species (Candida albicans) are regulated by TBF1. To gain insight into more general evolutionary mechanisms, we have created a mathematical algorithm that finds such general switching events and we prove that it converges. Of course any such computational discovery should be validated in the biological tests. For each branch of the phylogenetic tree and each gene module, our algorithm finds a sub-group of co-regulated genes and a team of transcription factors that substitutes for another team of transcription factors. In most cases the signal will be small but in some cases we find a strong signal of switching. We report our findings for 23 Ascomycota fungi species.