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.
Thanks for this analysis. I hope you are correct.