  To study a flavour model with a non-minimal Higgs sector one must first
define the symmetries of the fields; then identify what types of vacua exist
and how they may break the symmetries; and finally determine whether the
remnant symmetries are compatible with the experimental data. Here we address
all these issues in the context of flavour models with any number of Higgs
doublets. We stress the importance of analysing the Higgs vacuum expectation
values that are pseudo-invariant under the generators of all subgroups. It is
shown that the only way of obtaining a physical CKM mixing matrix and,
simultaneously, non-degenerate and non-zero quark masses is requiring the
vacuum expectation values of the Higgs fields to break completely the full
flavour group, except possibly for some symmetry belonging to baryon number.
The application of this technique to some illustrative examples, such as the
flavour groups Delta(27), A4 and S3, is also presented.
