If your response levels are ordered (like low, medium, high), then you can fit an ordinal logistic model. If they are unordered, then you can fit a nominal logistic model. Repeated measures can be accommodated in either. The ordinal model can be fit in the GLIMMIX or GENMOD procedures using the DIST=MULT option in the MODEL statement. In GLIMMIX, use the RANDOM statement to deal with repeated measures. In GENMOD, use the REPEATED statement. The nominal model can be fit in the GLIMMIX or GEE procedures by also adding the LINK=GLOGIT option in the MODEL statement. Note that these models are not "nonparametric" - they are using the multinomial distribution which is appropriate for a categorical response.