A statistical mechanical model of silica melt is presented in which metal oxides are incorporated into the bonding network. In this approach a Flory-type lattice model for binary silicate melts is coupled with a set of chemical reactions that determine the extent of metal oxide incorporation into the silica network and regulate the distribution of nonbridging oxygens around a central silicon. The theory produces two- and three-phase coexistence curves over a range of parameter space. The three-phase equilibrium regions coalesce to critical end points, where two of the three phases have become critical, and to a nonsymmetric tricritical point, where all three phases have simultaneously become critical. The theory captures the qualitative behavior and essential features of simple binary silicate melts.