Would it be possible...?

If Prince William and the Duchess of Cambridge end up having a lot of children, would it be possible for each of them to end up ruling a separate Commonwealth Realm in their own right as independent Kings and Queens? When the time comes, could the descendants of the future King William divide the Commonwealth between them, giving each country it's own head of state? For example, say if William and Kate have sixteen children, could one of them one day be King or Queen of Canada, while another becomes King or Queen of Australia, and another of Papua New Guinea, Jamaica, New Zealand, et cetera? Would this not give each country it's own unique Royal Family?