This is an interesting question, Lilo, but it's so improbable that it's difficult to answer:

First: any caporegime(s) or other conspirator(s) can murder the Don and attempt to take over. The issue is whether or not they have enough support in the family (and maybe in others) to stay in power. Even a cocoz' like Gotti consulted factions in the family, and key players in other families, before he had Castellano whacked, and Big Paul had given them plenty of provocation. As long as Vito was alive, he was all-powerful and commanded tremendous loyalty.

Second: The Corleones' top strength was Vito's political power, which seemed to be held exclusively by Vito. He was attempting to transfer it to Michael before he died, and I think his phrase (in the movie), "this wasn't enough time, Michael," reflected his fear that Michael would make his move .before he had all of Vito's political power "wired into him" (the novel's phrase).

Third: As Oli notes, creating a new family out of whole cloth is unprecedented and improbable. If Vito had given them permission, what would be left for Michael, the appointed heir? I'd add that there's never been a co-Donship in Mafia history, and never will be. Clem and Tess either would have formed two families out of their own territories, or fought each other to the death for sole proprietorship. Either would have fatally weakened both. I posted that in a thread:
http://www.gangsterbb.net/threads/ubbthreads.php?ubb=showflat&Number=574490&Searchpage=1&Main=20369&Words=%2Bstroke+%2Bof+%2Bgood+%2Bluck&Search=true#Post574490

That's why I believe Tessio's betrayal was a major stroke of good luck for Michael.