  In this paper, we extend the analysis of scanning the perturbatively flat
flux vacua (PFFV) for the type IIB orientifold compactifications on the mirror
of the projective complete intersection Calabi-Yau (pCICY) 3-folds, which are
realized as hypersurfaces in the product of complex projective spaces. We
present the PFFV statistics for all the 36 pCICYs with $h^{1,1}=2$ and classify
them into two categories of being K3-fibered model and non K3-fibered model. We
find that all the K3-fibered models have a significantly large number of PFFV
leading to physical vacua by fixing the axio-dilaton by non-perturbative
effects, while only a couple of non K3-fibered models have such physical vacua.
We have found that there are five pCICY $3$-folds with the suitable exchange
symmetry leading to the so-called exponentially flat flux vacua (EFFV) which
are protected against non-perturbative prepotential effects as well. Finally we
explored the underlying exchange symmetries in the favorable dataset of 7820
pCICYs and have found that there are only 15 spaces which can result in EFFV
configurations.
