  We discuss the phenomenological viability of string multi-Higgs doublet
models, namely a scenario of heterotic $Z_3$ orbifolds with two Wilson lines,
which naturally predicts three supersymmetric families of matter and Higgs
fields. We study the orbifold parameter space, and discuss the compatibility of
the predicted Yukawa couplings with current experimental data. We address the
implications of tree-level flavour changing neutral processes in constraining
the Higgs sector of the model, finding that viable scenarios can be obtained
for a reasonably light Higgs spectrum. We also take into account the tree-level
contributions to indirect CP violation, showing that the experimental value of
$\epsilon_K$ can be accommodated in the present framework.
