  We present a new type of counterexample to the Nelson-Seiberg theorem. It is
a generic R-symmetric Wess-Zumino model with nine chiral superfields, including
one field of R-charge 2 and no R-charge 0 field. As in previous
counterexamples, the model gives a set of degenerate supersymmetric vacua with
a non-zero expectation value for a pair of oppositely R-charged fields.
However, one of these fields appears quadratically in the superpotential, and
many other fields with non-zero R-charges gain non-zero expectation values at
the vacuum, and so this model escapes the sufficient condition for
counterexamples established in previous literature. Thus there are still open
problems in the relation of R-symmetries to supersymmetry breaking in generic
models.
