The ground-state projection version of the Hubbard-Stratonovich auxiliary-field simulation method has been extended to Hubbard-style models with arbitrary range interactions between pairs of sites. For repulsive interactions, a transformation based on three auxiliary fields per site performs comparably to the usual single-field approach for local interactions. These fields have unit-variance Gaussian distributions, and couple to the number operators on each site through several matrices calculated from the original pairwise interaction matrix. Tests of this approach have been performed on small clusters of sites representing highly simplified models of atoms and molecules. Our recently introduced ‘‘positive-projection’’ approximation remains effective in controlling the ‘‘sign problem.’’ Comparisons to exact diagonalization demonstrate that accurate energies and correlation functions are obtained using this approach.