  Recently it was shown that, in the framework of superstring inspired $\E$
models, the presence of generation dependent discrete symmetries allows us to
construct a phenomenologically viable class of models in which the three
generations of fermions do not have the same embedding within the fundamental
{\bf 27} dimensional representation of E$_6$. In this scenario, these different
embeddings of the conventional fermions imply that the left-handed charged
leptons and the right-handed $d$-type quarks are coupled in a non--universal
way to the new neutral gauge bosons $(Z_\theta)$ present in these models. It
was also shown that a unique signature for this scenario, would be a deviation
from unity for the ratio of cross sections for the production of two different
lepton species in $e^+e^-$ annihilation. However, several different scenarios
are possible, depending on the particular assignment chosen for $e_L$, $\mu_L$
and $\tau_L$ and for the right-handed $d$-type quarks, as well as on the type
of $Z_\theta$ boson. Such scenarios can not be disentangled from one another by
means of cross section measurements alone. In this paper we examine the
possibility of identifying the pattern of embeddings through measurements of
polarized and unpolarized asymmetries for fermion pair-production at the 500
GeV $e^+e^-$ Next Linear Collider (NLC). We show that it will be possible to
identify the different patterns of unconventional assignments for the
left-handed leptons and for the $b_R$ quark, for $Z_\theta$ masses as large as
$\sim 1.5$ TeV.
