The emergence of pathogenic bacteria resistant to multiple antibiotics is a serious worldwide public health concern. Whenever antibiotics are applied, the genes encoding for antibiotic resistance are selected for within bacterial populations. This has led to the prevalence of conjugative plasmids that carry resistance genes and can transfer themselves between diverse bacterial groups. In this study, we investigated whether it is feasible to attempt to prevent the spread of antibiotic resistances with a lytic bacteriophage, which can replicate in a wide range of gram‐negative bacteria harbouring conjugative drug resistance–conferring plasmids. The counter‐selection against the plasmid was shown to be effective, reducing the frequency of multidrug‐resistant bacteria that formed via horizontal transfer by several orders of magnitude. This was true also in the presence of an antibiotic against which the plasmid provided resistance. Majority of the multiresistant bacteria subjected to phage selection also lost their conjugation capability. Overall this study suggests that, while we are obligated to maintain the selection for the spread of the drug resistances, the ‘fight evolution with evolution’ approach could help us even out the outcome to our favour.