  In a previous paper we have proposed a non--Newtonian, phenomenological
description of the effective gravitational force acting between exotic dark
matter and baryons, which was shown to fit well the kinematics in the inner
regions of low surface brightness, gas--rich galaxies. The Gravitational
Suppression (GraS) scheme is, admittedly, an ad-hoc model; it does however
successfully address interesting cosmological issues. Here, we test the
potential generality of the GraS concept. GraS predictions on motions on scales
measurable in dwarf spheroidal galaxies and in the solar neighborhood show
significant departures from those of Newtonian mechanics. By analyzing such
systems, we find that the paradigm of a universal GraS potential cannot be
rejected. Indeed, compared to Newtonian predictions, GraS provides a better
description of data, when realistic dark matter density profiles are
considered.
