The large icy moons of Jupiter contain vast quantities of liquid water, a key ingredient for life. Ganymede and Callisto are weaker candidates for habitability than Europa, in part because of the model-based assumption that high-pressure ice layers cover their seafloors and prevent significant water–rock interaction. Water–rock interactions may occur, however, if heating at the rock–ice interface melts the high pressure ice. Highly saline fluids would be gravitationally stable, and might accumulate under the ice due to upward migration, refreezing, and fractionation of salt from less concentrated liquids. To assess the influence of salinity on Ganymede׳s internal structure, we use available phase-equilibrium data to calculate activity coefficients and predict the freezing of water ice in the presence of aqueous magnesium sulfate. We couple this new equation of state with thermal profiles in Ganymede׳s interior—employing recently published thermodynamic data for the aqueous phase—to estimate the thicknesses of layers of ice I, III, V, and VI. We compute core and silicate mantle radii consistent with available constraints on Ganymede׳s mass and gravitational moment of inertia. Mantle radii range from 800 to 900 km for the values of salt and heat flux considered here (4–44 mW m−2 and 0 to 10 wt% MgSO 4 ). Ocean concentrations with salinity higher than 10 wt% have little high pressure ice. Even in a Ganymede ocean that is mostly liquid, achieving such high ocean salinity is permissible for the range of likely S/Si ratios. However, elevated salinity requires a smaller silicate mantle radius to satisfy mass and moment-of-inertia constraints, so ice VI is always present in Ganymede׳s ocean. For lower values of heat flux, oceans with salinity as low as 3 wt% can co-exist with ice III. Available experimental data indicate that ice phases III and VI become buoyant for salinity higher than 5 wt% and 10 wt%, respectively. Similar behavior probably occurs for ice V at salinities higher than 10 wt%. Flotation can occur over tens of kilometers of depth, indicating the possibility for upward ‘snow’ or other exotic modes of heat and material transport.