  We systematically calculate the axion-photon coupling for non-minimal DFSZ
models. Thereby we can classify every calculated model and study the resulting
distributions, relevant for axion experiments like haloscopes, helioscopes or
light-shining-through-a-wall experiments. By adding more than one additional
Higgs doublet, these non-minimal DFSZ models extend the viable axion parameter
space and lead to a large range of axion-photon couplings. We find couplings
almost three orders of magnitude larger than the ones of the minimal models.
Most of the possible axion-photon couplings, however, lie in the vicinity of
the values dictated by the minimal models. We quantify this by introducing a
theoretical prior probability distribution for DFSZ-type axions and giving
$68\%$ and $95\%$ lower bounds as well as two-sided bands. We compare our
results for the DFSZ axion-photon coupling distributions with the KSVZ case,
for which a similar analysis has been conducted. Both display similar values as
well as a very specific pattern. In order to identify preferred models, we
discuss the role of flavour changing neutral currents and the domain wall
problem as possible selection criteria. It is possible to construct a large
number of non-minimal DFSZ models with a domain wall number of unity and
thereby avoiding the domain wall problem. This subset also has a significantly
enhanced axion-photon coupling compared to the minimal DFSZ models.
