Generalizing three-family chiral fermion conditions to Iac = −(3 + h) and \( {I}_{a{c}^{\prime }}=h \) , with positive integer h, we extend the landscape of three-family \( \mathcal{N}=1 \) supersymmetric Pati-Salam models in a broader region. Differing from the former investigation with Iac = −3 and \( {I}_{a{c}^{\prime }}=0 \) , we do not restrict that the a stack of D6-branes must be parallel to the orientifold image of the c-stack along one of the three two-tori. In this investigation, without the simple parallel construction, we find four new classes of supersymmetric Pati-Salam models that are allowed by the extended three generation condition with Iac = 3, \( {I}_{a{c}^{\prime }}=-6 \) and Iac = −1, \( {I}_{a{c}^{\prime }}=-2 \) through the intersections of a- and c/c′-branes. Moreover, with the \( \textrm{SU}{(2)}_{L^{\prime }} \) gauge coupling realized from \( \textrm{SU}{(2)}_{L_1}\times \textrm{SU}{(2)}_{L_2} \) symmetry breaking, the canonical normalization requirement of the gauge kinetic term provides an alternative approach that can be imposed before the renormalization group equation evolution for \( \textrm{SU}{(2)}_{L^{\prime }} \) gauge coupling. This turns out to be an effective mechanism to realize the string-scale gauge coupling relation, especially for the new supersymmetric Pati-Salam models with large gb/ga ratio. We show that this symmetry-breaking modified renormalization group evolution can highly suppress gb/ga, and finally realizes string-scale gauge coupling relations for the extended supersymmetric Pati-Salam models as well.
