  A three Higgs-doublet model admitting an $S_3$-symmetry can predict the
observed pattern of the quark masses and their mixings. However the same
symmetry also introduces potential flavour-changing neutral currents at the
tree level. We assume in this work that the scalar potential contains
appropriate \emph{soft} $S_3$-breaking terms in order to keep the choices of
the scalar masses flexible. We identify the parameters in the Yukawa Lagrangian
in the quark sector responsible for such FCNCs and constrain them using data
from some of the flavour physics observables like meson-decays and
meson-mixings. We also validate the corresponding model parameter space with
renormalisation group (RG) evaluation.
