Disjoint complete minors and bipartite minors

Let r, s and t be integers and let c(r) be such that every graph G with at least c(r)|G| edges has a K"r minor. We prove that there is a function f"r","s","t(n), with f"r","s","t(n)=o(n) as n->~, such that every graph of order n and having at least (c(r)+s-1)n+f"r","s","t(n) edges contains either t disjoint K"r minors or a K"s","t minor.