impeachment
"While judicial precedents inform the effective substantive meaning of various provisions of the Constitution, impeachment is at bottom a unique political process largely unchecked by the judiciary. While the meaning of treason and bribery is relatively clear, the scope of high crimes and misdemeanors lacks a formal definition and has been fleshed out over time, in a manner perhaps analogous to the common law, through the practice of impeachments in the United States Congress.
7 The type of behavior that qualifies as impeachable conduct, and the circumstances in which impeachment is an appropriate remedy for such actions, are thus determined by, among other things, competing political interests, changing institutional relationships among the three branches of government, and legislators’ interaction with and accountability to the public.8 The weight of historical practice, rather than judicial precedent, is thus central to understanding the nature of impeachment in the United States."
I assume you understand what this portends. There is precedent for impeaching a president just for thinly-disguised political reasons.
And you want to eliminate the illegal immigrant thing as grounds. I wonder why.