[eigen]

> For example, consider a president who dies in office a few days into the term. The VP becomes president, serves out the remainder of that four-year term and then be elected for two more terms

text of the 22nd amendment covers that. serving more than 2 years of someone else's term means you can only be elected once.

Section 1. 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.