The transfer matrix method developed for the study of monomer adsorption on terraces and nanotubes is applied to on top adsorption on fcc(112) stepped surfaces. The effect due to the step is taken into account by considering adsorbate-substrate interaction on step sites to be different from that on the other bulk sites. We also consider first-and second- neighbor adsorbate-adsorbate interactions, with attractive First-neighbors, thus completing the work published three years ago on repulsive first-neighbors. In the three-dimensional, low temperature energy phase diagram, other than empty and full coverage, there are eight phases: three cluster formations consisting of 4, 5, and 6 adatoms, and five stripe patterns parallel to the steps. Of the thirty-seven phases reported in the repulsive case, none exhibits clusters, and only four of them have stripes that match the ones found in the attractive case. These and other selection rules allow one to predict whether first-neighbors are attractive or repulsive, while the energy phase diagram can be used as a guide to obtain additional information oil the remaining interaction energies.