Our understanding of how antimicrobial resistance enzymes evolve to expand their substrate spectrum is limited. OXA-48, an enzyme able to catalyse the hydrolysis of β-lactam drugs, has become one of the most successfully disseminating β-lactamases. Although OXA-48 hydrolyses penicillins with high efficiency, its activity towards oxyimino cephalosporins, such as ceftazidime, is limited. Thus, ceftazidime and the combination of ceftazidime and the β-lactamase inhibitor avibactam, which inhibits OXA-48, are possible treatment options for infections caused by OXA-48 producing pathogens. Here, different evolutionary protocols were employed to elucidate the role of both ceftazidime and ceftazidime-avibactam as drivers in the evolution of OXA-48. Laboratory evolution towards increasing drug concentrations and long-term experimental evolution under low drug concentrations demonstrated that OXA-48 can acquire mutations that increase resistance to both ceftazidime and ceftazidime-avibactam. Independent replicates of directed evolution further showed that OXA-48 mediated ceftazidime resistance can be improved by the acquisition of only a few mutations, resulting in distinct mutational trajectories. Crystallographic structures demonstrated that increased resistance was likely achieved by optimising substrate positioning and the pre-organisation of active site residues. In addition, molecular dynamics simulations exposed elevated flexibility of active site loops, which likely aided the accommodation of ceftazidime. Studying epistatic and pleiotropic effects during the adaptational process uncovered that mutations, initially conferring increased ceftazidime resistance, tended to exhibit strong trade-offs concerning functionality and thermostability. However, the functional trade-off towards other β-lactams, such penicillins and carbapenems, was strong but limited due to positive epistasis among mutational combinations. Taken together, OXA-48-mediated ceftazidime and ceftazidime-avibactam resistance can evolve through point mutations and distinct mutational pathways. The diversity of these pathways in combination with epistasis has implications for the genotypic and phenotypic predictability of resistance development, as many mutational highly epistatic solutions may exist within an enzyme.