My read of the Constitution is that (if there was the political will) the U.S. House of Representatives could draw up and pass Articles of Impeachment for individuals in the Senate, to include the leadership. (What Constitutional amendment “locks out the HoR”? - correction welcomed!)
AND (if there was the political will) the Senate could try the impeachment and vote to remove the offenders from office...
But if they won’t even hold the current executive accountable for the innumerable violations of law it’s committed, do you think they’ll self police?
Article I§5: "Each House may determine the Rules of its Proceedings, punish its Members for disorderly Behaviour, and, with the Concurrence of two thirds, expel a Member
Article I§6; "...and for any Speech or Debate in either House, they shall not be questioned in any other Place."
Article II§4: "The President, Vice President and all civil Officers of the United States, shall be removed from Office on Impeachment for, and Conviction of, Treason, Bribery, or other high Crimes and Misdemeanors (Senators and Members of Congress are not "civil officers of the United States").
Article III§1: "The Judges, both of the supreme and inferior Courts, shall hold their Offices during good Behaviour".
Nothing in there could possibly allow the House to punish a Senator.
Each House may determine the Rules of it Proceedings, punish its members for disorderly Behaviour, and with the Concurrence of two-thirds, expel a member.