Highly Imbalanced dataset fro classes more than 200
The situation you describe is a few-shot learning problem: you have a lot of classes and only a few examples for some of them.

Similarity metric learning with siamese neural networks is well suited for this task. The idea is to learn a general similarity metric between examples, then classify new examples as belonging to the class of the "closest" sample from the training set. It seems a bit complex but it's probably the best way to learn "across" classes. 

The link I've shared above is applied to an NLP problem so should be able to reuse it fairly easily.