  Conventional superstring derived E$_6$ models can accommodate small neutrino
masses if a discrete symmetry is imposed which forbids tree level Dirac
neutrino masses but allows for radiative mass generation. Since the only
possible symmetries of this kind are known to be generation dependent, we
explore the possibility that the three sets of light states in each generation
do not have the same assignments with respect to the 27 of $E_6$, leading to
non universal gauge interactions under the additional $U(1)'$ factors for the
known fermions. We argue that models realising such a scenario are viable, with
their structure being constrained mainly by the requirement of the absence of
flavor changing neutral currents in the Higgs sector. Moreover, in contrast to
the standard case, rank 6 models are not disfavoured with respect to rank 5. By
requiring the number of light neutral states to be minimal, these models have
an almost unique pattern of neutrino masses and mixings. We construct a model
based on the unconventional assignment scenario in which (with a natural choice
of the parameters) $m_{\nut}\sim O(10)$eV is generated at one loop, $m_{\num}$
is generated at two loops and lies in a range interesting for the solar
neutrino problem, and $\nue$ remains massless. In addition, since baryon and
lepton number are conserved, there is no proton decay in the model. To
illustrate the non-standard phenomenology implied by our scheme we also discuss
a second scenario in which an attempt for solving the solar neutrino puzzle
with matter enhanced oscillations and practically massless neutrinos can be
formulated, and in which peculiar effects for the $\num$ --> $\nut$ conversion
of the upward-going atmospheric neutrinos could arise as well.
