  We consider an extension of the standard model (SM) with three $SU(2)$ scalar
doublets and a discrete $S_3\otimes \mathbb{Z}_2$ symmetries. The irreducible
representation of $S_3$ has a singlet and a doublet, and here we show that the
singlet corresponds to the SM-like Higgs and the two additional $SU(2)$
doublets forming a $S_3$ doublet are inert. In general, in a three scalar
doublet model, with or without $S_3$ symmetry, the diagonalization of the mass
matrices implies arbitrary unitary matrices. However, we show that in our model
these matrices are of the tri-bimaximal type. We also analyzed the scalar mass
spectra and the conditions for the scalar potential is bounded from below at
the tree level. We also discuss some phenomenological consequences of the
model.
