The Zdanovskii-Stokes-Robinson (ZSR) equation, or linear isopiestic relation, can be used to estimate osmotic and activity coefficients of multicomponent mixtures, based on the properties of pure (single solute) solutions. We have generalised an extension to the ZSR equation (for ternary mixtures) to systems containing an indefinite number of solutes, and derived the corresponding equations for solute activity coefficients. The new model is tested by calculating salt solubilities in Na+/NH4+/Cl-/SO42- aqueous solutions, liquid-liquid phase equilibrium in the acetone/glycerol/water system, and thermodynamic properties of aqueous NaCl/sucrose solutions (all at 298.15 K). The mixture parameters, up to three for each pair of solutes, significantly increase the accuracy of the method. It is least satisfactory for solutions containing both electrolytes and non-electrolytes, and it was found that the ZSR equation predicts activity coefficients of trace amounts of non-electrolytes in salt solutions that do not conform to the Setchenow relationship.