File suit with who? The constitution is clear who has the sole authority over impeachment trials.
And its not the judiciary.
File suit with SCOTUS.
The SCOTUS doesn't have any authority over impeachment trials.
"
The Senate shall have the sole Power to try all Impeachments. When sitting for that Purpose, they shall be on Oath or Affirmation."
The only role the judiciary plays in impeachments is that the Chief justice of the SCOTUS has to preside over any trial of the President.
That's it. Trump's not the president. And Roberts isnt presiding over his impeachment trial. So the judiciary plays ZERO role in Trump's impeachment trial. The authority to try impeachments lies solely with the Senate.