A new scheme analogous to that employed for the determination of the free energy of classical single-component systems, with arbitrary many-body interaction potentials at arbitrary densities and temperatures, is extended to classical multicomponent systems. Self-consistency of the scheme has been shown for some limiting, conditions, including the noninteraction limit. Thermodynamic expressions are obtained which are natural extensions of those for the single-component case and readily reduce to their correct forms in the single-component limit. Application to the simple case of low-density mixtures of hard particle gases in 3-D is outlined. It is expected (as in the single-component case) that progressive application to more complex systems (such as quantum mixed systems) will be done under a single mathematical framework, as provided in this paper.