Adhesion of charged toner particles used in electrophotography is dominated by electrostatic forces. In this paper we discuss a model which describes the process by which toner particles acquire their electrostatic charge, tribocharging. In previous papers, we have presented a model of tribocharging of two-component mixtures of powders based on the assumptions that: 1. The surface of each powder is populated with electron accepting and donating sites; 2. The density of states of the donating and accepting sites can be represented by narrow bands, all of which have the same energy; and 3. Charge is exchanged between donor and acceptor sites until thermodynamic equilibrium is established. In this paper, we show how to extend this model to multi-component mixtures. The extended model can be used to calculate the charging behavior of three-component mixtures of electrophotographic toners and carriers based on measurements with two component mixtures. Experimentally-measured charging behavior agrees with the model predictions. These results confirm it is possible to assign charging site densities to individual materials empirically. The site densities can then be used to predict charging behavior of the materials in mixtures which have not been studied experimentally. The success of the model also implies that toner particles migrate freely from carrier particle to carrier particle and that triboelectric interactions take place between toner particles of different compositions in mixtures.