  We consider a classical lattice gas that consists of more than one "species"
of particles (like a spin-3/2 Ising model or the atomic limit of the extended
Hubbard model), whose ground-state phase diagram is macroscopically degenerate.
This gas is coupled component-wise and in the Falicov-Kimball-like manner to a
multicomponent free-fermion gas. We show rigorously that a component-wise
coupling of the classical subsystem to the quantum one orders the classical
subsystem so that the macroscopic degeneracy is removed.
