  We extend the classification of fermionic $\mathbb{Z}_2\times\mathbb{Z}_2$
heterotic string orbifolds to non--supersymmetric Pati--Salam (PS) models in
two classes of vacua, that we dub $\tilde S$--models and $S$--models. The first
correspond to compactifications of a tachyonic ten--dimensional vacuum, whereas
the second correspond to compactifications of the ten--dimensional
tachyon--free $SO(16)\times SO(16)$ heterotic string. In both cases we develop
a systematic method to extract tachyon--free four--dimensional models. We show
that tachyon--free configurations arise with probability $\sim0.002$ and
$\sim0.01$ in the first and second case, respectively. We adapt the `fertility
methodology' that facilitates the extraction of phenomenological models. We
show that Pati--Salam $\tilde S$--models do not contain heavy Higgs scalar
representations that are required to break the PS symmetry to the Standard
Model and are therefore not phenomenologically viable. Hence, we argue that in
$\tilde S$--models the $SO(10)$ GUT symmetry must be broken at the string scale
to the Standard--like Model subgroup. We extract tachyon--free three generation
models in both cases that contain an equal number of massless bosonic and
fermionic degrees of freedom, ${\it i.e.}$ with $a_{00}=N_b^0-N_f^0=0$, and
analyse their one--loop partition function.
