Could Barack Obama run as a vice president or is that also illegal? I mean, if he ran as Hillary Clinton's VP, then Hillary resigned, he would be president again, right?
The limit on ELECTED officials per the 22nd amendment is a maximum 8 years. If the president were to die in office or not be able to function, BO would probably be able to achieve more service through the second way, SUCCESSION which as far as I'm aware doesn't have the same limit as Elected does.
At least again as far as I've read up on it. The other school of thought is that he would remain VP(being illegible for presidency) and the Speaker of the House would ascend to the presidency instead.
The third school of thought says no, because a VP must be eligible for presidency and a president serving 2 terms is not eligible for re assuming the presidency.
The constitution is really really weird on it. People tend to agree that it could happen, but no one wants to test those waters.