The effects of solid-solid phase changes on subsolidus convection in the large icy moons of the outer solar system are considered. Phase transitions affect convection via processes that distort the phase change boundary and/or influence buoyancy through thermal expansion. Linear stability analyses are carried out for ice layers with a phase change at the midplane. Two exothermic phase transitions (ice I-ice II, ice VI-ice VIII) and two endothermic transitions (ice I - ice II, ice VI - ice VIII) and two endothermic transitions (ice I-ice III, ice II-ice V) are considered. For the exothermic cases, the phase change can either impede or enhance whole-layer convection. For the endothermic cases, the phase change always inhibits whole-layer convective overturn and tends to enforce two-layer convection. These results place same constraints on possible models of icy satellite evolution and structure.