Most ecosystems provide multiple services, thus the impact of biodiversity losses on ecosystem functions may be considerably underestimated by studies that only address single functions. We propose a multivariate modelling framework for quantifying the relationship between biodiversity and multiple ecosystem functions (multifunctionality). Our framework consolidates the strengths of previous approaches to analysing ecosystem multifunctionality and contributes several advances. It simultaneously assesses the drivers of multifunctionality, such as species relative abundances, richness, evenness and other manipulated treatments. It also tests the relative importance of these drivers across functions, incorporates correlations among functions and identifies conditions where all functions perform well and where trade‐offs occur among functions. We illustrate our framework using data from three ecosystem functions (sown biomass, weed suppression and nitrogen yield) in a four‐species grassland experiment. We found high variability in performance across the functions in monocultures, but as community diversity increased, performance increased and variability across functions decreased.