  We describe a class of three Higgs doublet models (3HDMs) with a softly
broken $\mathrm{U}(1) \times \mathrm{U}(1)$ family symmetry that enforces a
Cabibbo-like quark mixing while forbidding tree-level flavour changing neutral
currents. The hierarchy in the observed quark masses is partly explained by a
softer hierarchy in the vacuum expectation values of the three Higgs doublets.
As a consequence, the physical scalar spectrum contains a Standard Model (SM)
like Higgs boson $h_{125}$ while exotic scalars couple the strongest to the
second quark family, leading to rather unconventional discovery channels that
could be probed at the Large Hadron Collider. In particular, we describe a
search strategy for the lightest charged Higgs boson $H^{\pm}$, through the
process $c\bar s\to H^{+}\to W^+\,h_{125}$, using a multivariate analysis that
leads to an excellent discriminatory power against the SM background. Although
the analysis is applied to the proposed class of 3HDMs, we employ a
model-independent formulation such that it can be applied to any other model
with the same discovery channel.
