This mechanic currently seems a big bugged or at least badly implemented. I was called in by my ally into his war and, even though we're both in the same war (and it's his war, a defensive one on top) I can not call him to other wars because he "would be called to multiple wars". That makes no sense whatsoever. Since the UI for war declaration has been improved upon so much, I'd personally love a simple addition: tickers into which wars you want to call your allies. That would allow you to have several wars at the same time, while still being able to call your allies for one of them.
EDIT: And it's even worse because the AI does not take the new co-belligerent mechanic into account. If I'm called to war by Ally A but not named co-belligerent and I want to declare my own war, I can not call any allies because of "would be called to multiple wars" - even though I'm not allowed to do so anyway, because I'm no co-belligerent. Don't get me wrong: the new system is infinitely better than the old one, but there're some parts that do not work in a logical or reasonable way.