  Let $G$ be a multipartite graph with partition $V_1, V_2,\ldots, V_k$ of
$V(G)$. Let $d_{i,j}$ denote the edge density of the pair $(V_i, V_j)$. An
independent transversal is an independent set of $G$ with exactly one vertex in
each $V_i$. In this paper, we prove an asymptotically sharp upper bound on the
maximum number of independent transversals given the $d_{i,j}$'s.
