In response to many of the comments above, indeed you can only max 3 classes for desyn. However, you don't really need max on any class for anything specific at the moment. In fact, at this point of the game, there's no specific reason to get pass even level 70 yet (except breaking gear to clear inventory).

Personally, I have 2 classes above 310, 1 class above 280 and 1 class around level 70. So yeah, I have four classes. My forth class is BSM. I just find it useful for breaking down Mog items from Thornmarch. Will classes above 300 be useful for anything specific in the future? We have no idea yet...

To answer the OP's question, different classes rarely share the same kind of items for optimal desyn training. Some "shared" items include those items from Silver Bazaar:


as well as those items from GC:


But the ones in GC don't cover all classes... Furthermore, each class has their own desyn items before they can reach a point where it is optimal to desyn the above items.

GSM is one of the easiest one, imo. Especially when Aetheryte Ring (i55) being only needing 1 Rose Gold Nugget. So you practically get back that 1 nugget at 100% rate.... completely recycled all mats (except catalyst).