SMOTE for multilabel classification
If you have only one example for certain classes SMOTE won't work. Most of the Machine Learning algorithms won't work either.

There is a technique called One Shot Learning (it is normally used in computer vision) that  "Whereas most machine learning-based object categorization algorithms require training on hundreds or thousands of samples/images and very large datasets, one-shot learning aims to learn information about object categories from one, or only a few, training samples/images."

Maybe you could try with one OSL to help you with the classification but normal ML algorithms require more samples to be able to generalize.