Magma supply rate from depth to the summit at Kīlauea volcano, Hawai'i is not constant through time. Even during the current Pu'u 'Ō'ō-Kupaianaha eruption (1983-present), a surge in supply occurred from 2003-2007. This surge was accompanied by summit inflation, increased CO2 emissions, and finally culminated in a dike intrusion and surface eruption. Recent work has suggested that a surge in supply is a result of an increase in dissolved volatiles in the melt zone. Alternatively, the surge could come from a mechanical change in the melt zone, perhaps as an increase in permeability or melt production. I develop a numerical model of two-phase flow between the melt zone and summit at Kīlauea to explore the role of volatile composition, conduit geometry, and pressure in the melt zone on supply rate. Results suggest that volatiles have a limited role in increasing supply, a dike-shaped conduit is likely, and pressure increases in the melt zone drive changes in supply. Additionally, a dike-shaped conduit yields a decoupling of conditions at the surface from those at depth, which impacts how conditions in the mantle below Kīlauea are inferred from surface deformation and summit gas emissions.