The statistical mechanical basis of the use of Brunauer-Emmett-Teller isotherms to represent activities and other thermodynamic properties in extremely concentrated solutions was established by Ally and Braunstein (J. Chem. Thermodynamics 1998, 30, 49-58) for a two-salt, single-solvent, mixture. Based upon the work of these authors, we have derived equations for solute and solvent activities in liquid mixtures containing a single solvent and indefinite number of solutes. New terms have been added to the model equations to express the effects of ternary ion interactions on the salt adsorption parameters. Solution composition is defined on the basis of salts, rather than ions, as components. As examples, the model is used to represent water activities in concentrated (lithium nitrate + potassium nitrate + water) and (lithium ion + sodium ion + chloride ion + nitrate ion + water) mixtures, and salt solubilities in (calcium chloride + calcium nitrate + water) mixtures.