  In hierarchical evolutionary scenarios, isolated, physical pairs may
represent an intermediate phase, or "way station", between collapsing groups
and isolated elliptical (E) galaxies (or fossil groups). We started a
comprehensive study of a sample of galaxy pairs composed of a giant E and a
spiral (S) with the aim of investigating their formation/evolutionary history
from observed optical and X-ray properties. Here we present VLT-VIMOS
observations designed to identify faint galaxies associated with the E+S
systems from candidate lists generated using photometric criteria on WFI images
covering an area of ~ 0.2 h^{-1} Mpc radius around the pairs.
  The results are discussed in the context of the evolution of poor galaxy
group associations. A comparison between the Optical Luminosity Functions
(OLFs) of our E+S systems and a sample of X-ray bright poor groups suggest that
the OLF of X-ray detected poor galaxy systems is not universal. The OLF of our
X-ray bright systems suggests that they are more dynamically evolved than our
X-ray faint sample and some X-ray bright groups in the literature. However, we
suggest that the X-ray faint E+S pairs represent a phase in the dynamical
evolution of some X-ray bright poor galaxy groups. The recent or ongoing
interaction in which the E member of the X-ray faint pairs is involved could
have decreased the luminosity of any surrounding X-ray emitting gas.
