Statistical–mechanical description of multi-layer surface segregation in multi-component alloys, based on the free-energy concentration expansion method (FCEM), is introduced. The generalized FCEM provides simple analytical expressions for numerical minimization of the alloy free energy in the presence of short-range order (SRO).As an example, this theoretical approach is applied to unravel segregation with site competition at the (1 1 1) surface of a ternary Ni–8 at.%Al–4 at.%Cu(1 1 1) solid solution. Compared to the corresponding Ni–Al and Ni–Cu binary alloys, the calculations predict significant enhancement of Cu surface segregation and Al desegregation due to the relatively strong Ni–Al attractive interactions and SRO effects. A compositional phase transition marks the onset of Al segregation at high temperatures.