Plasmids have a key role in the horizontal transfer of genes among bacteria. Although plasmids are catalysts for bacterial evolution, it is challenging to understand how they can persist in bacterial populations over the long term because of the burden they impose on their hosts (the 'plasmid paradox'). This paradox is especially perplexing in the case of 'small' plasmids, which are unable to self-transfer by conjugation. Here, for the first time, we investigate how interactions between co-infecting plasmids influence plasmid persistence. Using an experimental model system based on interactions between a diverse assemblage of 'large' plasmids and a single small plasmid, pNI105, in the pathogenic bacterium Pseudomonas aeruginosa, we demonstrate that positive epistasis minimizes the cost associated with carrying multiple plasmids over the short term and increases the stability of the small plasmid over a longer time scale. In support of these experimental data, bioinformatic analysis showed that associations between small and large plasmids are more common than would be expected owing to chance alone across a range of families of bacteria; more generally, we find that co-infection with multiple plasmids is more common than would be expected owing to chance across a wide range of bacterial phyla. Collectively, these results suggest that positive epistasis promotes plasmid stability in bacterial populations. These findings pave the way for future mechanistic studies aimed at elucidating the molecular mechanisms of plasmid-plasmid interaction, and evolutionary studies aimed at understanding how the coevolution of plasmids drives the spread of plasmid-encoded traits.