The trick with repeal of the 22nd Amendment is that any President popular enough within his own party to run for a third term will scare the other party enough that they won't support repeal. It'd take a herculean effort to find someone popular enough on both sides of the aisle to justify a repeal applicable to the current President.
The most likely form of repeal would be an amendment that splits the middle, something like this (many thanks to Lord Grattan for the bulk of the text, I hope you don't mind me copying rather than retyping it all):
"The Twenty-second Article of Amendment to the Constitution of the United States is hereby repealed.
Any person eligible to hold the office of President of the United States, or act as President, may be elected to the office of President any number of times. Any person who has held the office of President of the United States for two full consecutive terms shall be ineligible to serve as President for the following term. This Article shall become operative immediately upon its ratification, but shall be inoperative unless it shall have been ratified as an amendment to the Constitution by the legislatures of three-fourths of the several states within seven years from the date of its submission to the states by the Congress."
This provides for repeal of the 22nd, which members of both major parties have attempted to do in every Congress, without enabling a three, four, or more-term Presidency, and would not appear to be enacted for any particular candidate.
This amendment might also include language to allow naturalized citizens to serve as President, which has also been a popular potential reform to the office.