  We study the electroweak and $U(1)^{'}$ symmetry breaking patterns in models
with the particle content of supersymmetric $E_{6}$, including standard model
singlets $S$ and exotic quarks $D,~\bar{D}$. Motivated by free fermionic string
models, we do not require $E_{6}$-type relations between Yukawa couplings. In
particular, we assume that baryon and lepton numbers are conserved, so that the
exotic quarks can be light. Gauge invariance allows Yukawa interactions between
$S$ and Higgs doublets, and between $S$ and the exotic quarks, allowing
radiative $U(1)^{'}$ symmetry breaking and the generation of an effective $\mu$
parameter at the electroweak scale. For both the $E_{6}$ $\psi$ and $\eta$
models, universal soft supersymmetry breaking parameters and Yukawa
universality at the high (string) scale do not yield acceptable low energy
phenomenology. Relaxing universality, we find solutions with phenomenologically
acceptable values of $M_{Z^{'}}$ and the $Z-Z^{'}$ mixing angle. In addition,
by varying the $U(1)^{'}$ charge assignments due to the mixing of $U(1)_{\chi}$
and $U(1)_{\psi}$ of $E_{6}$, it is possible to have acceptable low energy
phenomenology with universal boundary conditions.
