Genetic diversity often enhances the tolerance of microbial communities against antimicrobial treatment. However the sociobiology underlying this antimicrobial tolerance remains largely unexplored. Here we analyze how inter-species interactions can increase antimicrobial tolerance. We apply our approach to 17 industrially relevant multispecies biofilm models, based on species isolated from 58 contaminating biofilms in three breweries. Sulfathiazole was used as antimicrobial agent because it showed the highest activity out of 22 biofilm inhibitors tested. Our analysis reveals that competitive interactions dominate among species within brewery biofilms. We show that antimicrobial treatment can reduce the level of competition and therefore cause a subset of species to bloom. The result is a 1.2-42.7-fold lower percentage inhibition of these species and increased overall tolerance. In addition, we show that the presence of Raoultella can also directly enhance the inherent tolerance of Pseudomonas to antimicrobial treatment, either because the species protect each other or because they induce specific tolerance phenotypes as a response to competitors. Overall, our study emphasizes that the dominance of competitive interactions is central to the enhanced antimicrobial tolerance of the multispecies biofilms, and that the activity of antimicrobials against multispecies biofilms cannot be predicted based on their effect against monocultures.