I'm not an SAS Enterprise Miner user, so my response is more toward general SAS procedures.
What you are describing is a logistic regression with a nominal outcome. SAS LOGISTIC will not do that analysis, it can only do binary or ordinal logistic regressions.
Even if Enterprise Miner can do nominal logistic regression, it may not be able to create a stable model using the SEMMA approach. To get stable estimates requires about 15 observations per potential predictor for the rarest outcome. With 20 outcomes, you will run up against a sample size limitation on the SEMMA limit of 32,000 obserations.
You are probably going to have to collapse your outcomes and either get to an ordinal scale or a series of binaries.