Biodiversity is proposed to be important for the rate of ecosystem functions. Most biodiversity-ecosystem function studies, however, consider only one response variable at a time, and even when multiple variables are examined they are analyzed separately. This means that a very important aspect of biodiversity is overlooked: the possibility for different species to carry out different functions at any one time. We propose a conceptual model to explore the effects of species loss on overall ecosystem functioning, where overall functioning is defined as the joint effect of many ecosystem functions. We show that, due to multifunctional complementarity among species, overall functioning is more susceptible to species loss than are single functions. Modeled relationships between species richness and overall ecosystem functioning using five empirical data sets on monocultures reflected the range of effects of species loss on multiple functions predicted by the model. Furthermore, an exploration of the correlations across functions and the degree of redundancy within functions revealed that multifunctional redundancy was generally lower than single-function redundancy in these empirical data sets. We suggest that by shifting the focus to the variety of functions maintained by a diversity of species, the full importance of biodiversity for the functioning of ecosystems can be uncovered. Our results are thus important for conservation and management of biota and ecosystem services.