A neat point about the Italian Ambition mission is that the reward is given, as with all other missions, slightly after fulfilling the criteria. This means that you can offer several simultaneous peace demands for territory and get cores on all of them, even if they're from several different nations - given that none is war leader over any other. You could always keep some country wholly occupied until you're ready to peace all Italian states out simultaneously. Do try to get some infamy-decreasing cb before going for it though, for obvious reasons.