Ecosystem resistance to a single stressor relies on tolerant species that can compensate for sensitive competitors and maintain ecosystem processes, such as primary production. We hypothesize that resistance to additional stressors depends increasingly on species tolerances being positively correlated (i.e. positive species co‐tolerance). Initial exposure to a stressor combined with positive species co‐tolerance should reduce the impacts of other stressors, which we term stress‐induced community tolerance. In contrast, negative species co‐tolerance is expected to result in additional stressors having pronounced additive or synergistic impacts on biologically impoverished functional groups, which we term stress‐induced community sensitivity. Therefore, the sign and strength of the correlation between species sensitivities to multiple stressors must be considered when predicting the impacts of global change on ecosystem functioning as mediated by changes in biodiversity.