Copper-based membrane-electrode assemblies (Cu-MEAs) hold promise for increasing the energy efficiency for the electrochemical reduction of CO₂ to C₂₊ products, while maintaining high current densities. However, fundamental understanding of Cu-MEAs is still limited compared to the wealth of knowledge available for aqueous-electrolyte Cu systems. Physics-based modeling can assist in the transfer of knowledge from aqueous to vapor-fed systems by deconvoluting the impacts of various physical processes and accelerating the optimization of Cu-MEAs. Here, we simulate Cu-MEA performance and describe how the change in cell architecture leads to changes in cell performance and optimization. Our results reveal nonuniformity of product distribution in the catalyst layer, allowing us to explore catalyst-layer properties as design parameters for increasing the energy efficiency of C₂₊ product formation. We discuss multiphase flow and water-management issues and show how membrane properties, specifically the electro-osmotic coefficient, affect the efficacy of feeding liquid water to hydrate the membrane. Finally, we explore tradeoffs associated with operating Cu-MEAs at 350 K in order to increase the supply of water and the preferential formation of products with higher activation energies (typically C₂₊ products).