Antibiotics that have multiple cellular targets theoretically reduce the frequency of resistance evolution, but adaptive trajectories and resistance mechanisms against such antibiotics are understudied. Here we investigate these in methicillin resistantStaphylococcus aureus(MRSA) using experimental evolution upon exposure to delafloxacin (DLX), a novel fluoroquinolone that targets both DNA gyrase and topoisomerase IV. We show that selection for coding sequence mutations and genomic amplifications of the gene encoding a poorly characterized efflux pump, SdrM, leads to high DLX resistance, circumventing the requirement for mutations in both target enzymes. In the evolved populations,sdrMoverexpression due to genomic amplifications containingsdrMand two adjacent genes encoding efflux pumps results in high DLX resistance, while the adjacent hitchhiking efflux pumps contribute to streptomycin cross-resistance. Further, lack ofsdrMnecessitates mutations in both target enzymes to evolve DLX resistance, andsdrMthus increases the frequency of resistance evolution. Finally,sdrMmutations and amplifications are similarly selected in two diverse clinical isolates, indicating the generality of this DLX resistance mechanism. Our study highlights that instead of reduced rates of resistance, evolution of resistance to multi-targeting antibiotics can involve alternate high-frequency evolutionary paths, that may cause unexpected alterations of the fitness landscape, including antibiotic cross-resistance.