Ecosystem multifunctionality (EMF), the simultaneous provision of multiple ecosystem functions, is often affected by biodiversity and environmental factors. We know little about how the interactions between biodiversity and environmental factors affect EMF. In this case study, a structural equation model was used to clarify climatic and geographic pathways that affect EMF by varying biodiversity in the Tibetan alpine grasslands. In addition to services related to carbon, nitrogen, and water cycling, forage supply, which is related to plant productivity and palatability, was included in the EMF index. The results showed that 72% of the variation in EMF could be explained by biodiversity and other environmental factors. The ratio of palatable richness to all species richness explained 8.3% of the EMF variation. We found that air temperature, elevation, and latitude all affected EMF, but in different ways. Air temperature and elevation impacted the aboveground parts of the ecosystem, which included plant height, aboveground biomass, richness of palatable species, and ratio of palatable richness to all species richness. Latitude affected EMF by varying both aboveground and belowground parts of the ecosystem, which included palatable species richness and belowground biomass. Our results indicated that there are still uncertainties in the biodiversity–EMF relationships related to the variable components of EMF, and climatic and geographic factors. Clarification of pathways that affect EMF using structural equation modeling techniques could elucidate the mechanisms by which environmental changes affect EMF.