Bacteria live in dynamic systems where selection pressures can alter rapidly, forcing adaptation to the prevailing conditions. In particular, bacteriophages and antibiotics of anthropogenic origin are major bacterial stressors in many environments. We previously observed that populations of the bacterium Pseudomonas fluorescens SBW25 exposed to the lytic bacteriophage SBW25Φ2 and a noninhibitive concentration of the antibiotic streptomycin (coselection) achieved higher levels of phage resistance compared to populations exposed to the phage alone. In addition, the phage became extinct under coselection while remaining present in the phage alone environment. Further, phenotypic tests indicated that these observations might be associated with increased mutation rate under coselection. In this study, we examined the genetic causes behind these phenotypes by whole‐genome sequencing clones isolated from the end of the experiments. We were able to identify genetic factors likely responsible for streptomycin resistance, phage resistance and hypermutable (mutator) phenotypes. This constitutes genomic evidence in support of the observation that while the presence of phage did not affect antibiotic resistance, the presence of antibiotic affected phage resistance. We had previously hypothesized an association between mutators and elevated levels of phage resistance under coselection. However, our evidence regarding the mechanism was inconclusive, as although with phage mutators were only found under coselection, additional genomic evidence was lacking and phage resistance was also observed in nonmutators under coselection. More generally, our study provides novel insights into evolution between univariate and multivariate selection (here two stressors), as well as the potential role of hypermutability in natural communities.