We present a finite-size scaling study of a centered rectangular lattice-gas model with attractive nearest-neighbor interactions and repulsive second- and third-neighbor and three-particle interactions, as well as attractive fifth-neighbor interactions. This has been proposed as a model for atomic oxygen adsorbed on a (110) surface of tungsten. The ordered phases are a (2×1) phase with coverage 12 and a (2×2) phase with coverage 34. We obtain phase diagrams which are in good qualitative agreement with the available experimental information. This agreement is obtained with considerably weaker attractive fifth-neighbor interactions than previously suggested by ground-state and Monte Carlo calculations, but consistent with the results of quantum-mechanical band calculations. In particular, we find a multicritical point below which the low-coverage (2×1)-to-disorder transition is of first order. We also find indications of a previously undetected low-temperature multicritical point below which the high-coverage (2×2)-to-disorder transition may be of first order. The finite-size effects in this study are considerably stronger than in previous studies of simpler lattice-gas models. This limits the accuracy with which we can determine the multicritical temperatures. It also prevents us from obtaining reliable estimates of the nonuniversal critical exponents for this model.