We use conjugation to investigate the linkage and potential for horizontal transfer of a limited number of clusters of antibiotic resistance genes that dominate the Extended-Spectrum Beta-Lactamase antibiotic resistance gene landscape in samples of Extraintestinal E. coli recovered from two West Coast hospitals. These include: a) an integron with two aminoglycoside phosphotransferases b) two functionally-overlapping groups genes, encompassing diverse β-lactamases and aminoglycoside acetyltransferases in combinations of up to 4 genes that we name AG1 and AG2 for “association group 1 and 2”. We characterize 139 sequenced, multidrug resistant clinical strains from two different hospitals for the ability to transfer carbenicillin resistance by conjugation. We made the following observations: a) β-lactamase-bearing conjugative plasmids largely (95%) belonged to the IncF plasmid incompatibility group and 97% of these have combinations of IncF replicons; b) AG1 and AG2 gene combinations can spread by conjugation but this is not consistently the case; higher-order combinations tend to appear in non-conjugating strains. The observed patterns of conjugation transfer of CG1 and CG2 genes suggest that conjugation plays an important role in the early stages of evolution of multidrug resistance, making genes available for the generation of adaptive solutions, and that these adaptive solutions are highly heterogeneous, driven by selection rather than by co-mobilization. In fact, our results suggest that the formation of more complex combinations occurs at the expense of their ability to be mobilized.