Considering ice-premelting on a quartz rock surface (i.e. silica) we calculate the Lifshitz excess pressures in a four layer system with rock–ice–water–air. Our calculations give excess pressures across (1) ice layer, (2) water layer, and (3) ice–water interface for different ice and water layer thicknesses. We analyse equilibrium conditions where the different excess pressures take zero value, stabilized in part by repulsive Lifshitz interactions. In contrast to previous investigations which considered varying thickness of only one layer (ice or water), here we present theory allowing for simultaneous variation of both layer thicknesses. For a given total thickness of ice and water, this allows multiple alternative equilibrium solutions. Consequently the final state of a system will depend on initial conditions and may explain variation in experimental measurements of the thicknesses of water and ice layers.