Thermodynamic methods are used to obtain the conditions of mechanical equilibrium for a system consisting of two bulk phases meeting at an interface containing two surface phases separated by a line discontinuity. Under conditions for which the stable system contains only one particular surface phase, the real system may be in a metastable state where the interface is occupied by a surface phase which does not exist in the stable state. In this circumstance, the existence of a line tension at a line discontinuity is sufficient to hinder the formation of the stable surface phase. Relations are obtained between the temperature, pressure and bulk phase composition at which either or both surface phases exist in a stable system. Estimates of the line tension, and quantities associated with the formation of critical sized patches of the stable surface phase are made for the system water + phloroglucinol dihydrate + NaCl at pressures between 1 and 3500 bars.