We consider symmetric binary mixtures consisting of spherical particles with equal diameters interacting via a hard-core plus attractive tail potential with strengths epsilon(ij), i,j=1,2, such that epsilon(11)=epsilon(22)>epsilon(12). The phase diagram of the system at all densities and concentrations is investigated as a function of the unlike-to-like interaction ratio delta=epsilon(12)/epsilon(11) by means of the hierarchical reference theory. The results are related to those of previous investigations performed at equimolar concentration, as well as to the topology of the mean-field critical lines. As delta is increased in the interval 0<delta<1, we find first a regime where the phase diagram at equal species concentration displays a tricritical point, then one where both a tricritical and a liquid-vapor critical point are present. We did not find any clear evidence of the critical end point topology predicted by mean-field theory as delta approaches 1, at least up to delta=0.8, which is the largest value of delta investigated here. Particular attention was paid to the description of the critical-plus-tricritical point regime in the whole density-concentration plane. In this situation, the phase diagram shows, in a certain temperature interval, a coexistence region that encloses an island of homogeneous, one-phase fluid.