Binary M2Ag6, M2Ag7, M1Ag7 and M1Ag8 clusters (M = Cu, Au, Pd) adsorbed on an MgO(100) terrace presenting a double vacancy (DV) neutral defect are investigated through a combination of density-functional (DF) biased searches and global optimizations. Alloying allows one to probe the adsorption characteristics of the DV-defected surface. It is found that Au1Ag7 and Au2Ag6 are core-shell magic clusters, in analogy with the pure silver case. The magic character is reduced for Cu1Ag7 and Cu2Ag6, because the shortening of Cu-Ag distances is counteracted by a double-frustration effect due to the DV, and is practically absent for Pd1Ag7 and Pd2Ag6, because the requirements of the metallic bond conduction electron count are in conflict with the metal-surface interaction. However, fluxionality is enhanced for Pd-Ag clusters with respect to the pure silver case, which could influence their catalytic properties.