A remarkably tight relation is observed between the Newtonian gravity sourced by the baryons and the actual gravity in galaxies of all sizes. This can be interpreted as the effect of a single, effective force law depending on acceleration. This is, however, not the case in larger systems with much deeper potential wells such as galaxy clusters. Here we explore the possibility of an effective force law reproducing mass discrepancies in all extragalactic systems when depending on both acceleration and the deepness of the potential well. We exhibit, at least at a phenomenological level, one such possible construction in the classical gravitational potential theory. The framework, dubbed extended modified Newtonian dynamics, is able to reproduce the observed mass discrepancies in both galaxies and galaxy clusters, and to produce multicenter systems with offsets between the peaks of gravity and the peaks of the baryonic distribution.