The physical requirement for charge to balance across biological membranes means that the transmembrane transport of each ionic species is interrelated, and manipulating solute flux through any one transporter will affect other transporters at the same membrane, often with unforeseen consequences. The OnGuard systems modeling platform has helped to resolve the mechanics of stomatal movements, uncovering previously unexpected behaviors of stomata. To date, however, the manual approach to exploring model parameter space has captured little formal information about the emergent connections between parameters that define the most interesting properties of the system as a whole. Here, we introduce global sensitivity analysis to identify interacting parameters affecting a number of outputs commonly accessed in experiments in Arabidopsis (Arabidopsis thaliana). The analysis highlights synergies between transporters affecting the balance between Ca2+ sequestration and Ca2+ release pathways, notably those associated with internal Ca2+ stores and their turnover. Other, unexpected synergies appear, including with the plasma membrane anion channels and H+-ATPase and with the tonoplast TPK K+ channel. These emergent synergies, and the core hubs of interaction that they define, identify subsets of transporters associated with free cytosolic Ca2+ concentration that represent key targets to enhance plant performance in the future. They also highlight the importance of interactions between the voltage regulation of the plasma membrane and tonoplast in coordinating transport between the different cellular compartments.