The rate of modern drug discovery using experimental screening methods still lags behind the rate at which pathogens mutate, underscoring the need for fast and accurate predictive simulations of protein evolution. Multidrug-resistant bacteria evade our defenses by expressing a series of proteins, the most famous of which is the 29-kilodalton enzyme, TEM β-lactamase. Considering these challenges, we applied a covalent docking heuristic to measure the effects of all possible alanine 237 substitutions in TEM due to this codon's importance for catalysis and effects on the binding affinities of commercially-available β-lactam compounds. In addition to the usual mutations that reduce substrate binding due to steric hindrance, we identified two distinctive specificity-shifting TEM mutations, Ala237Arg and Ala237Lys, and their respective modes of action. Notably, we discovered and verified through minimum inhibitory concentration assays that, while these mutations and their bulkier side chains lead to steric clashes that curtail ampicillin binding, these same groups foster salt bridges with the negatively-charged side-chain of the cephalosporin cefixime, widely used in the clinic to treat multi-resistant bacterial infections. To measure the stability of these unexpected interactions, we used molecular dynamics simulations and found the binding modes to be stable despite the application of biasing forces. Finally, we found that both TEM mutants also bind strongly to other drugs containing negatively-charged R-groups, such as carumonam and ceftibuten. As with cefixime, this increased binding affinity stems from a salt bridge between the compounds' negative moieties and the positively-charged side chain of the arginine or lysine, suggesting a shared mechanism. In addition to reaffirming the power of using simulations as molecular microscopes, our results can guide the rational design of next-generation β-lactam antibiotics and bring the community closer to retaking the lead against the recurrent threat of multidrug-resistant pathogens.