We investigate the doping process theoretically for singly doped MAu24, MAg24, and MAu37 (M = Ni, Pd, Pt, Cu, Ag/Au, Zn, Cd, Hg, Ga, In, and Tl) clusters using density functional theory (DFT). For all clusters, the group X dopants (Ni, Pd, and Pt) prefer the central location due to the relative stability of d electrons in the dopant. For dopants in groups XI-XIII, doping on the surface of the core and the ligand shell in MAu24 becomes thermodynamically more preferable as a result of symmetry-dictated coupling between dopant atomic orbitals and superatomic levels as well as because of relativistic contraction of s and p orbitals. The same mechanisms are also found to be responsible for the relative isomer energies in MAu37 clusters. For these clusters, DFT calculations predict that it is unlikely for the dopant atom to occupy the central location. We found similar trends for different dopants across the periodic table in relative isomer energies of MAu24 and MAg24; however, center-doped clusters are somewhat more stable in the case of MAg24 due to the smaller relativistic stabilization of s and p levels in Ag compared to Au. We also found that the metallic radii of the dopant can affect the geometries and relative stabilities of the isomers for the doped clusters significantly.