Increase in mass of a NS, will reduce its size and stabilize. If this reduction is such that R(p) is encountered then the energy will release and again stabilize (after reduction in mass) till no longer R(p) is challenged. Yes, the innermost core of a Neutron Star can have exotic matter (quarks etc). The mass of a Neutron is 940 MeV and the total rest mass of three constituent quarks is 12 Mev. Hope now you can parse it.