Maybe it's the fact that I've only been awake less than an hour, but wouldn't just Same Franchise suffice?
You spoke of Leijiverse being a Same Universe relation, but even then it's all under the name Leijiverse, right? (Unless there's something I'm not getting here.) Thus it's still all the same franchise though maybe not directly related to different series.
There's only one thing I can see with using same universe: Cross-overs. Lupin III vs. Detective Conan would be an example. But then again, does marking that as Same Universe imply that Lupin III and Conan are both in the same universe? But you need a way to related the characters back to their own series.
And then there's the case of Tsubasa Chronicle and XXXHolic. Do they count as the same franchise? I never watched XXXHolic and only a little of Tsubasa but I hear they're related, though not necessarily in the same universe (due to dimension hopping) but the same timeline and some character interaction (so maybe they make one giant universe?), if I have my facts straight.
And on a side note, Tsubasa Chronicle has Cardcaptor Sakura stuff listed in the relations. It uses the same characters but definitely not in the same universe or franchise.
Erm... I don't know if I helped or made things more complicated but I'm just throwing some stuff out there and hoping to hit with something...
