The energetics and kinetic energy barriers of vacancy/atom exchange in a 37-atom truncated octahedron Ag-Pt binary cluster in the Ag-rich range of compositions are investigated via a first-principles atomistic approach. The energy of the local minima obtained considering various distributions of a single vacancy and a few Pt atoms within the cluster and the energy barriers connecting them are evaluated using accurate density-functional calculations. The effects of the simultaneous presence of a vacancy and Pt atoms are found to be simply additive when their distances are larger than first-neighbors, whereas when they can be stabilizing at low Pt content due to the release of strain by the Pt/vacancy interaction or destabilizing close to a perfect Pt(core)/Ag(shell) arrangement. It is found that alloying with Pt appreciably increases the barriers for homotops transformations, thus rationalizing the issues encountered at the experimental level in producing Ag-Pt equilibrated nanoparticles and bulk phase diagram.