Good strategies for hierarchical classification with many classes

I'm working in a hierarchical multi class problem, and if I flat the labels (flat approach) I have about 1193 classes, which perhaps can already be consider a extreme multi classification problem. Furthermore, per class I have less than 10 examples per unique class.

With so many classes, I can't go with pairs for all combination, because it will result in a huge amount of pairs and I'm a bit limit in hardware and time.

Also, since is hierarchical I think it would work better if I privilege pairs with examples with the same "father", because I want to have a good discrimination even between example within the same "father" category.

Do you know any good strategy to this kind of problem? Perhaps train first between some random picked high level hierarchy and then further training with pairs that share the same root?