The functional diversity of enzyme families is thought to have been caused by repeated recruitment events--gene duplications followed by conversions to new functions. However, mathematical models show this can only work if beneficial new functions are achievable by just one or two base changes in the duplicate genes. Having found no convincing demonstration that this is feasible, we previously chose a highly similar pair of E. coli enzymes from the GABA-aminotransferase-like (GAT) family, 2-amino-3-ketobutyrate CoA ligase (Kbl2) and 8-amino-7-oxononanoate synthase (BioF2), and attempted to convert the first to perform the function of the second by site-directed mutagenesis. In the end we were unable to achieve functional conversion by that rational approach. Here we take a complementary approach based on random mutagenesis. Focusing first on single mutations, we prepared mutated libraries of nine genes from the GAT family and tested for BioF2 function in vivo. None of the singly mutated genes had this function. Focusing next on double mutations, we prepared and tested 70% of the 6.5 million possible mutation pairs for Kbl2 and for BIKB, an enzyme described as having both Kbl2 and BioF2 activities in vitro. Again, no BioF2 activity was detected in vivo. Based on these results, we conclude that conversion to BioF2 function would require at least two changes in the starting gene and probably more, since most double mutations do not work for two promising starting genes. The most favorable recruitment scenario would therefore require three genetic changes after the duplication event: two to achieve low-level BioF2 activity and one to boost that activity by overexpression. But even this best case would require about 10^15 years in a natural population, making it unrealistic. Considering this along with the whole body of evidence on enzyme conversions, we think structural similarities among enzymes with distinct functions are better interpreted as supporting shared design principles than shared evolutionary histories.