Theoretical interest in the distributions of species abundances observed in ecological communities has focused recently on the results of models that assume all species are identical in their interactions with one another, and rely upon immigration and speciation to promote coexistence. Here we examine a one-trophic level system with generalized species interactions, including species-specific intraspecific and interspecific interaction strengths, and density-independent immigration from a regional species pool. Comparisons between results from numerical integrations and an approximate analytic calculation for random communities demonstrate good agreement, and both approaches yield abundance distributions of nearly arbitrary shape, including bimodality for intermediate immigration rates.