Losses and gains in species diversity affect ecological stability(1-7) and the sustainability of ecosystem functions and services(8-13). Experiments and models have revealed positive, negative and no effects of diversity on individual components of stability, such as temporal variability, resistance and resilience(2,3,6,11,12,14). How these stability components covary remains poorly understood(15). Similarly, the effects of diversity on overall ecosystem stability(16), which is conceptually akin to ecosystem multifunctionality(17,18), remain unknown. Here we studied communities of aquatic ciliates to understand how temporal variability, resistance and overall ecosystem stability responded to diversity (that is, species richness) in a large experiment involving 690 micro-ecosystems sampled 19 times over 40 days, resulting in 12,939 samplings. Species richness increased temporal stability but decreased resistance to warming. Thus, two stability components covaried negatively along the diversity gradient. Previous biodiversity manipulation studies rarely reported such negative covariation despite general predictions of the negative effects of diversity on individual stability components(3). Integrating our findings with the ecosystem multifunctionality concept revealed hump- and U-shaped effects of diversity on overall ecosystem stability. That is, biodiversity can increase overall ecosystem stability when biodiversity is low, and decrease it when biodiversity is high, or the opposite with a U-shaped relationship. The effects of diversity on ecosystem multifunctionality would also be hump- or U-shaped if diversity had positive effects on some functions and negative effects on others. Linking the ecosystem multifunctionality concept and ecosystem stability can transform the perceived effects of diversity on ecological stability and may help to translate this science into policy-relevant information.