  Inspired by a recently proposed GUT model based on the trinification
($\mathrm{SU}(3)^3$) gauge group with a global family ($\mathrm{SU}(3)_F$)
symmetry, we consider an effective low-energy three Higgs doublet model that
may shed light on what underlies the observed fermion mass hierarchies and CKM
mixing. We discuss possibilities for charged scalars coming from this model to
show in collider experiments and show some interesting benchmark points.
