Though interspecific competition profoundly changes community structure and structural stability (species stable coexistence), the current theory does not properly incorporate interspecific competition in mutualistic systems. Inspired by multilayer network theory, here we develop a framework that takes into account interspecific competition derived from and varied with shared mutualists (see Fig. 1 for a minimal model of the proposed framework). Using theoretical and numerical analyses, we show that when competition is weighted and mediated by mutualistic interactions, the necessary conditions for the structural stability of mutualistic communities are radically altered, which gives rise to new stability transitions and bifurcations. Additionally, our results suggest a shift from global to local network properties when assessing the effect of network architectures on biodiversity and system’s feasibility. We show that species richness and maximum number of mutualists explain more than 90% of variations in structural stability, while nestedness and connectance have a negligible additive effect.