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Only if their actual objective were removal of the President ... something not even AOC could possibly believe will happen.
But logic means nothing to communists, as indicated by their wildly insane policies such as the "Green New Deal," open borders and turning major cities into open latrines where crooks are given all respect and police are vilified.
IN A NUTSHELL: If the House of Representatives continues completely rogue, perhaps continues to add fictitious charges to faux impeachments and batter the Senate with them, THEN HOW ARE THEY TO BE STOPPED?
They may have found a way to get the Constitutional process to shake itself to pieces ... and thus we win every battle but lose the war.
I am certainly no Constitutional scholar (thus pinging Defiant), but as I understand it the power of the SCOTUS was partly self-created, in Marbury v. Madison. Stepping out beyond these boundaries would be problematical for SCOTUS especially at this extremely divided point in our history.
I am worried about the potential that the RATs wish to deliberately provoke a destructive Constitutional crisis which will leave America weaker as a nation; and, that the merits or lack thereof of their insane impeachment efforts may have little bearing on the outcome.
Which is why it is so important to prove the collusion (we can see so clearly!) with this impeachment and be on top of any further attempts!
Evidence is presented that will destroy the sitting members of the House.
SCOTUS got their nose under the tent once...unfortunately it goes against them sticking it under the tent again
https://en.wikipedia.org/wiki/Nixon_v._United_States
It seems your question is how to handle a situation where the House continues sending over ridiculous impeachment charges, seriatum instead of all at once. Scotus does not need to get involved, although it potentially could. POTUS floated the idea of a suit against the House to claim that the articles sent over do not state impeachable offenses. The Court could hear that case, or decide that it does not have power to judge what the House impeaches for. Either way it would not threaten our Constitutional system.
The other thing that would result is that the Senate would get perturbed, and just start rejecting them without consideration as soon as they are voted by the House. They may do that with this first set of charges is acted on. If the House sends more, McConnell will respond with something showing his contempt.