Deposition of monolayers of strong electron donors or acceptors on metal surfaces in many cases results in a metal-independent work function as a consequence of Fermi-level pinning. This raises the question whether in such a situation molecular dipoles, which are also frequently used to tune the interface energetics, still can have any impact. We use density functional theory to show that the spatial position of the dipoles is the determining factor and that only dipoles outside the immediate metal-molecule interface allow work-function changes beyond the pinning limit.