We extend the classification of free fermionic heterotic-string models to vacua in which the SO(10) GUT symmetry is broken at the string level to the Pati-Salam subgroup. Using our classification method we recently presented the first example of a quasi-realistic heterotic-string vacuum that is free of massless exotic states. Within this method we are able to derive algebraic expressions for the Generalised GSO (GGSO) projections for all sectors that appear in the models. This facilitates the programming of the entire spectrum analysis in a computer code. The total number of vacua in the class of models that we classify is 251~1015. We perform a statistical sampling in this space of models and extract 1011 GGSO configurations with Pati-Salam gauge group. Our results demonstrate that one in every 106 vacua correspond to a three generation exophobic model with the required Higgs states, needed to induce spontaneous breaking to the Standard Model.