  The hierarchical reference theory (HRT) and the self-consistent
Ornstein-Zernike approximation (SCOZA) are two liquid state theories that both
furnish a largely satisfactory description of the critical region as well as
the phase coexistence and equation of state in general. Furthermore, there are
a number of similarities that suggest the possibility of a unification of both
theories. Earlier in this respect we have studied consistency between the
internal energy and free energy routes. As a next step toward this goal we here
consider consistency with the compressibility route too, but we restrict
explicit evaluations to a model whose exact solution is known showing that a
unification works in that case. The model in question is the mean spherical
model (MSM) which we here extend to a generalized MSM (GMSM). For this case, we
show that the correct solutions can be recovered from suitable boundary
conditions through either of SCOZA or HRT alone as well as by the combined
theory. Furthermore, the relation between the HRT-SCOZA equations and those of
SCOZA and HRT becomes transparent.
