Does a Caliphate need to be one single country?

Assalamualaikum wa rahmatullahi wa barakatuh. Just thinking out loud here. In theory, the khalifah is supposed to be the one main leader for the whole Ummah, right? But when we look back at history, it wasn't always like that. We had the Umayyads in Cordoba, the Fatimids, the Abbasids-all at the same time sometimes. So my question is, from a traditional Islamic perspective, does a caliphate have to be one single nation under one government? Or could it be more like a union where different Muslim countries come together under one khalifah but still keep their own borders and governments? Like a shared leadership thing while each stays independent. Would love to hear your thoughts. JazakAllahu khairan!