Whilst it's not possible to have different hierarchies within the same instance, it is possible to have different issue types that different projects use at that level.
So for example, let's say that I add a level called "Initiative" above "Epic". I can create two different issue types called "TeamA_Initiative" and "TeamB_Initiative" and associate each issue type with the project that those teams use (this does of course require that each team uses different projects!) and then make both of those new issue types be mapped to the Initiative hierarchy Level.
If "TeamA_Initiative" is only associated with "ProjectA" (and "ProjectA is only used by Team A) then Team A will have have their own type at that next hierarchy level.
Hopefully that makes sense?