Predicting evolutionary paths to antibiotic resistance is key for understanding and controlling drug resistance. When considering a single final resistant genotype, epistatic contingencies among mutations restrict evolution to a small number of adaptive paths. Less attention has been given to multi-peak landscapes, and while specific peaks can be favoured, it is unknown whether and how early a commitment to final fate is made. Here we characterize a multi-peaked adaptive landscape for trimethoprim resistance by constructing all combinatorial alleles of seven resistance-conferring mutations in dihydrofolate reductase. We observe that epistatic interactions increase rather than decrease the accessibility of each peak; while they restrict the number of direct paths, they generate more indirect paths, where mutations are adaptively gained and later adaptively lost or changed. This enhanced accessibility allows evolution to proceed through many adaptive steps while delaying commitment to genotypic fate, hindering our ability to predict or control evolutionary outcomes.