  It is known that a three Higgs doublet model (3HDM)symmetric under an exact
$A_4$ symmetry is not compatible with nonzero quark masses and/or
non-block-diagonal CKM matrix. We show that a 3HDM with softly broken $A_4$
terms in the scalar potential does allow for a fit of quark mass matrices.
Moreover, the result is consistent with $m_h=125\textrm{GeV}$ and the $h
\rightarrow WW, ZZ$ signal. We also checked numerically that, for each point
that passes all the constraints, the minimum is a global minimum of the
potential.
