It's an interesting question that comes up now and again. I don't know of any writings on nominal growth - do others know? Perhaps it is because nominal is different from binary and ordinal where the latter can be seen has having a single underlying continuous latent response variable, in that sense a single growth curve, and therefore a single slope when regressed on a predictor such as a growth factor. Nominal has as many slopes as there are categories minus 1, so that many growth curves.
Given no (applied) writings on it, it is harder to work with and publish. I would probably recommend instead working with a latent transition model, where you focus on the probabilities of transitioning from one category to another.