Comprehensive computer simulations of a tracer particle hopping in a lattice where the sites could be either empty or occupied by one or two background particles are performed using a standard Monte Carlo technique. The results for the diffusion coefficient are compared with those of a mean-field theory derived from a random-walk approach. The blocking effects due to dynamical background particles are obtained exactly. The correlation effects due to many-particle interactions are analyzed qualitatively. This kind of double-occupancy model can be applied to the study of ionic conduction in glasses.