  The Nambu--Jona-Lasinio model with two flavors, three colors and diquark
interactions is analyzed in the context of optimized perturbation theory (OPT).
Corrections to the thermodynamical potential that go beyond the large-$N_c$
(LN) approximation are taken into account, and the region of the phase diagram
corresponding to intermediate chemical potentials and very low temperatures is
explored. The simultaneous presence of both the quark-antiquark and diquark
condensates can cause the system to behave as a fluid composed of a
Bose-Einstein condensate (BEC) or a color superconductor one, in the form of a
Bardeen-Cooper-Schrieffer (BCS) superfluid. The BEC-BCS crossover is then
studied in the nonperturbative OPT scheme. The results obtained in the context
of the OPT method are then contrasted with those obtained in the LN
approximation. We show that there are values for the coupling constants related
to quark-quark and quark-antiquark interactions where the corrections beyond LN
brought by the OPT method can influence the behavior of the diquark condensate
and the effective quark mass as a function of the baryon chemical potential.
These changes in the behavior of the phase structure of the model modify the
location of the critical point related to the phase structure as a whole of the
model. Also, when we impose the color neutrality condition, our results show
that the nature of the phase transition can change as well, shifting the ratio
of the quark-antiquark and quark-quark interactions to higher values in the OPT
case as compared to the LN approximation.
