  We construct a multiscalar and non-renormalizable model where the
$\mathbf{S}_{3}$ flavor symmetry drives mainly the Yukawa couplings. In the
quark sector, the Nearest Neighbor Interaction (NNI) textures are behind the
CKM mixing matrix so that this is fitted in good agreement with the last
available results. In the lepton sector, an almost diagonal charged lepton mass
matrix and extended Fritzsch mass textures in the effective neutrino mass
matrix, that comes from the type II see-saw mechanism, provide consistent
values for the mixing angles where the normal hierarchy is favored. The model
predicts a CP-violating phase consistent with the experimental data and the BR
for the lepton flavor violation process, $\mu\rightarrow e\gamma$, is well
below the current bound.
