Twenty-second Amendment to the United States Constitution
The amendment prohibits any individual who has been elected president twice from being elected again. Under the amendment, an individual who fills an unexpired presidential term lasting greater than two years is also prohibited from winning election as president more than once. Scholars debate whether the amendment prohibits affected individuals from succeeding to the presidency under any circumstances or whether it only applies to presidential elections.
Dual mandate
Also typically permitted is for one person to seek multiple offices at the same level of government in the same election, although attempting to simultaneously seek multiple offices in the same branch of government (e.g. a sitting U.S. Representative seeking re-election to the House "and" election to the U.S. Senate) is severely frowned on and prohibited in many states (the constitutionality of these prohibitions is uncertain). Recent examples include three 2000 and 2012 presdential elections where Senator Joe Lieberman and Representative Paul Ryan respectively sought re-election and election to the vice presidency - neither was elected vice president, but both were re-elected to the offices in which they were the incumbents.