  We search for supersymmetric standard model realizations with extra singlets
and extra $ U(1)$ using the heterotic string compactification on the $
Z_{6-II}$ orbifold with two Wilson lines. We analyze the vacuum restabilization
mechanism for three representative Pati-Salam string models obtained in the
literature and present detailed results for the effective superpotential
compatible with the string selection rules. An automated selection of
semi-realistic vacua along flat directions in the non-Abelian singlet modes
field space is performed by requiring the presence of massless pairs of
electroweak Higgs bosons having trilinear superpotential couplings with
massless singlet modes and the decoupling of color triplet exotic modes needed
to suppress $B $ and $ L $ number violating processes.
