Interatomic Coulombic Decay (ICD) is an ultrafast energy transfer process. Via ICD, an excited atom can transfer its excess energy to a neighboring atom which is thus ionized. On the example of NeHeNe cluster, we recently reported [Phys. Rev. Lett. 119, 083403 (2017)] that the total ICD widths are substantially enhanced in the presence of an ICD inactive atom. The enhancement occurs due to the coupling of the resonance state to intermediate virtual states of the bridge atom-a mechanism named superexchange ICD. In this follow-up work, we analyze the partial ICD widths in NeHeNe cluster and show that only some channels are affected by the superexchange ICD process. Furthermore, we consider superexchange ICD in NeHeAr. We show that in this system the enhancement is still present but the energy transfer mediated by the superexchange mechanism is less efficient than in NeHeNe owing to the different ionization potentials of Ar and Ne. The behavior of the computed ICD widths is explained with a simple model based on first-order perturbation theory and a Hartree-Fock-like description of the states.