  It is well-known that three-family supersymmetric Pati-Salam models from
intersecting D6-branes, where either one or both of the ${\rm U}(2)$ gauge
factors are replaced by a ${\rm USp}(2)$ group, are quite scarce. In order to
construct all such kind of models with generic additional gauge symmetries, we
fix the observable sectors and study all the possible hidden sectors. Thus, we
are able to completely determine all types of such kind of the inequivalent
models on a $\mathbb{T}^6/(\mathbb{Z}_2\times \mathbb{Z}_2)$ orientifold from
IIA string theory. We find the gauge coupling relations to be highly sensitive
to the variations in the hidden sector. One of the models exhibits the gauge
coupling unification for a particular solution at the string scale. In
addition, we perform scan on the hidden sector variations for the models
presented in arXiv:2112.09632, whose gauge coupling relations are still
preserved. Thus, we fix the gap in the previous study and complete the model
building for all the inequivalent models.
