User blog:Edwin Shade/A Question About the SKI-Calculus

Recently I have read the article on the Xi function, and I have a question pertaining to the combinatory logic used in evaluating sequences of combinators, it is thus:

Seeing as one can model the B,C,K,W system, (which utilizes four combinators), in the SKI-system, (which uses three combinators), then would a function which diagonolizes over the number of combinators in a system such as SKI be only as powerful as SKI ? That is, can SKI represent any possible combinatorical logical system with n-combinators ?

I would appreicate an answer to this in the comments.