SMOTE-NC does not help to oversample my mixed continuous/categorical dataset
Before going through the process of oversampling, always see if the implementation of your algorithm supports assigning different weights to individual classes. The sklearn RandomForestClassifier has for example a class_weights parameter with which you can do that. I found this method to work better than over- or undersampling.

Also, I have to add an obligatory part: if you minority classes have only very few samples so that the charachteristics of the respective classes are not well captured, there is little you can do except collecting more data.