We apply the relative weights method to SU(3) gauge theory with staggered fermions of mass 695 MeV at a set of temperatures in the range 151 ≤ T ≤ 267 MeV, to obtain an effective Polyakov line action at each temperature. We then apply a mean field method to search for phase transitions in the effective theory at finite densities. The result is a transition line in the plane of temperature and chemical potential, with an end point at high temperature, as expected, but also a second end point at a lower temperature. We cannot rule out the possibilities that a transition line reappears at temperatures lower than the range investigated, or that the second end point is absent for light quarks.