Pourbaix diagrams have been used extensively to evaluate stability regions of materials subject to varying potential and pH conditions in aqueous environments. However, both recent advances in high-throughput material exploration and increasing complexity of materials of interest for electrochemical applications pose challenges for performing Pourbaix analysis on multidimensional systems. Specifically, current Pourbaix construction algorithms incur significant computational costs for systems consisting of four or more elemental components. Herein, we propose an alternative Pourbaix construction method that filters all potential combinations of species in a system to only those present on a compositional convex hull. By including axes representing the quantities of H+ and e- required to form a given phase, one can ensure every stable phase mixture is included in the Pourbaix diagram and reduce the computational time required to construct the resultant Pourbaix diagram by several orders of magnitude. This new Pourbaix algorithm has been incorporated into the pymatgen code and the Materials Project website, and it extends the ability to evaluate the Pourbaix stability of complex multicomponent systems.