There may be a loophole in the SECOND amendment, but the TWENTY-SECOND amendment is pretty clear:
"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 President more than once. But this Article shall not apply to any person holding the office of President when this Article was proposed by Congress, and shall not prevent any person who may be holding the office of President, or acting as President, during the term within which this Article becomes operative from holding the office of President or acting as President during the remainder of such term."
It even answers some questions I had, like if Trump died today and Pence would take over, if he could be elected twice or once as he did serve in somebody else's term... Since the period is now less than 2 years before Trump's term ends that would be twice, in this hypothesis.