The evolution of new protein functions is dependent upon inherent biophysical features of proteins. Whereas, it has been shown that changes in protein dynamics can occur in the course of directed molecular evolution trajectories and contribute to new function, it is not known whether varying protein dynamics modify the course of evolution. We investigate this question using three related ß-lactamases displaying dynamics that differ broadly at the slow timescale that corresponds to catalytic turnover yet have similar fast dynamics, thermal stability, catalytic, and substrate recognition profiles. Introduction of substitutions E104K and G238S, that are known to have a synergistic effect on function in the parent ß-lactamase, showed similar increases in catalytic efficiency toward cefotaxime in the related ß-lactamases. Molecular simulations using Protein Energy Landscape Exploration reveal that this results from stabilizing the catalytically-productive conformations, demonstrating the dominance of the synergistic effect of the E014K and G238S substitutions in vitro in contexts that vary in terms of sequence and dynamics. Furthermore, three rounds of directed molecular evolution demonstrated that known cefotaximase-enhancing mutations were accessible regardless of the differences in dynamics. Interestingly, specific sequence differences between the related ß-lactamases were shown to have a higher effect in evolutionary outcomes than did differences in dynamics. Overall, these ß-lactamase models show tolerance to protein dynamics at the timescale of catalytic turnover in the evolution of a new function.