Pressure-driven transport of ternary electrolyte solutions has been considered within the scope of irreversible thermodynamics. At small thermodynamic forces, a general solution for an n-ionic system has been obtained and, further, specified and examined for a ternary system with a common colon. With the help of the continuous version of irreversible thermodynamics, two further limiting cases have been considered, namely, one of large Peclet numbers and one of a small addition of one of the electrolytes. Thermodynamic results have been exemplified within the scope of the capillary space-charge model. Parameters which govern the separation of counterions have been examined as functions of fixed charge density, pore size, feed ionic strength, the ratio of counterion mobilities and charges. A significant separation of counterions with different mobilities and/or charges was predicted.