  A binary lattice gas model that allows for multiple occupancy of lattice
sites, inspired by recent coarse-grained descriptions of solutions of
interacting polymers, is investigated by combining the steepest descent
approximation with an exploration of the multidimensional energy landscape, and
by Gibbs ensemble Monte Carlo simulations. The one-component version of the
model, involving on site and nearest neighbour interactions, is shown to
exhibit microphase separation into two sub-lattices with different mean
occupation numbers. The symmetric two-component version of the multiple
occupancy lattice gas is shown to exhibit a demixing transition into two phases
above a critical mean occupation number.
