Much effort has been directed at developing models for the computer simulation of liquid water. The simplest models involve effective two-molecule interactions, parametrized from experiment, for use in classical molecular dynamics simulations. These models have been very successful in describing the structure and dynamics of liquid water at room temperature and one atmosphere pressure. A completely successful model, however, should be robust enough to describe the properties of liquid water at other thermodynamic points, water's complicated phase diagram, heterogeneous situations like the liquid/vapor interface, ionic, and other aqueous solutions, and confined and biological water. In this paper, we develop a new classical simulation model with explicit three-molecule interactions. These interactions presumably make the model more robust in the senses described above, and since they are short-ranged, the model is efficient to simulate. The model is formulated as a perturbation from a classical two-molecule interaction model, where the forms of the correction to the two-molecule term and the three-molecule terms result from electronic structure calculations on dimers and trimers. The magnitudes of these perturbations, however, are determined empirically. The resulting model improves upon the well-known two-molecule interaction models for both static and dynamic properties.