Sorry StnCld, the 22nd amendment to the Constitution deals with the term of the President--However, given the make up of Congress---IMO it just would not happen and
he would not get support from 3/4 majority of the States.
What would it take to repeal the 22nd Amendment?
So, yes, Trump could absolutely push for a repeal of the current limit. Off the back of a strong State of the Union and personal best approval rating, he might even garner enough support. It would require a two-thirds majority proposal in the Senate or the House. States would then have to ratify the amendment with a three-quarters majority.
The odds are against him, though. A Constitutional repeal has only happened once, to repeal the 18th Amendment which established Prohibition.
It’s difficult and unlikely, but not impossible.