The Free-energy Concentration Expansion Method (FCEM) was utilized for the prediction of compositional structures in Ni – Cu – Rh cubo-octahedron nanoclusters in comparison to recently reported Ni – Cu – Pd data. While both systems exhibit site-specific, sequentially competitive surface segregation (and resultant core separations), remarkable differences governed by the opposite heteronuclear effective interactions, were noted in the surface compositional patterns. Thus, at relatively low temperatures "mixed" Cu/Pd ordering takes place at the Ni – Cu – Pd cluster surface, whereas in the Ni – Cu – Rh cluster Cu and Ni populate separate low and high-coordinated surface sites, thus forming a kind of "demixed surface order". Dissimilarities in the temperature dependence are discussed in terms of the interplay of segregation and compositional order. Such findings may have implications in heterogeneous catalysis and other technologies based on highly dispersed alloyed particles.