  We examine a non-reversible, mean-field Potts model with three spins on a set
with $N\uparrow\infty$ points. Without an external field, there are three
critical temperatures and five different metastable regimes. The analysis can
be extended by a perturbative argument to the case of small external fields. We
illustrate the case of large external fields with some phenomena which are not
present in the absence of external field.
