The phase structure and concentration dependence of the lattice parameter and energy of formation of ternary Pd–Ti–X and Pt–Ti–X alloys for a large number of ternary alloying additions X (X = Na, Mg, Al, Si, Sc, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Y, Zr, Nb, Mo, Tc, Ru, Rh, Ag, Cd, Hf, Ta, W, Re, Os, Ir) are investigated with an atomistic modeling approach. In addition, a detailed description of the site preference behavior of such additions showing that the elements can be grouped according to their absolute preference for a specific site, regardless of concentration, or preference for available sites in the deficient sublattice is provided.