12th Amendment.
Section 1 of Article Two of the United States Constitution sets forth the eligibility requirements for serving as president of the United States:
No Person except a natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution, shall be eligible to the Office of President; neither shall any person be eligible to that Office who shall not have attained to the Age of thirty five Years, and been fourteen Years a Resident within the United States.
The 12h Amendment lists qualifications, but does not mention the two election limit. So the 12th is not a disqualifier in and of itself.
Moving on to the 22nd Amendment: No person shall be elected to the office of the President more than twice, and no person who has held the office of President, or acted as President, for more than two years of a term to which some other person was elected President shall be elected to the office of the President more than once.
That amendment states only that an eligible person cannot be
elected more than twice.
It is interesting that the authors of the amendment did not simplify the law by stating that no individual could serve more than eight years as President rather than focusing on the issue of election.
In my thinking, I agree with several here that see loopholes in the law that a dominant political party could use to force their candidate into serving more than two terms.