The resonant-Auger - interatomic Coulombic decay (ICD) cascade was recently suggested as an efficient means of controlling the course of the ICD process. Recent theoretical and experimental works show that control over the energies of the emitted ICD electrons can be achieved either by varying the photon energy to produce different initial core excitations or by changing the neighboring species. This work presents a theoretical investigation on the role of the rare-gas neighbor and clarifies how the latter influences the ICD process. For this purpose, we compare fully ab initio computed ICD-electron and kinetic energy release spectra following the 2p(3/2) → 4s, 2p(1/2) → 4s and 2p(3/2) → 3d of Ar in ArKr and Ar2. We demonstrate that the presence of the chemically "softer" partner atom results in an increase in the energies of the emitted ICD electrons, and also in the appearance of additional ICD-active states. The latter leads to a threefold increase in the ICD yield for the case of the 2p(3/2, 1/2) → 4s parent core excitations.