The oxygen reduction reaction (ORR) is an important reaction for fuel cells. Mo-doped octahedral Pt3Ni nanoparticles have been recently reported to have very high ORR specific activity and stability. We have constructed a computational model to better understand the effects of composition, size, and doping 3d transitional metals (such as Mo) on octahedral particles at the atomic scale. For Pt-Ni-Mo nanoparticles, we demonstrate a cluster expansion approach based on ab-initio calculations to investigate the structure and stability of Pt-Ni-Mo octahedral nanoparticles. With this cluster expansion approach, at the atomic level, we identify the preferred positions of Pt, Ni, and Mo atoms within the alloy nanoparticles, and we investigate how the existence of Mo atoms will stabilize the Ni and Pt atoms on different surface sites (fcc, edge and vertex sites) against dissolution. We also investigate how doped Mo atoms improve the ORR activity.