I don't think the States have the ability to add new mechanisms to remove Senators or Congressmen, because the rules are set in the Constitution. It would require an amendment to change.
That is why we don't have term limits. Several States passed term limits in the 1980s, but the Supreme Court ruled they were unconstitutional because the "complete requirements" for the office are laid out in the Constitution, and States are not free to add more to them, nor to modify them.
Refusing to seat people is a method that has been used for keeping undesirables out of the Congress.
However it too was ruled unconstitutional by the Supreme Court in 1969 in the case of Adam Clayton Powerll.
Unseated members of the United States Congress
Both houses of the United States Congress have refused to seat new members based on Article I, Section 5 of the United States Constitution which states that, "Each House shall be the judge of the elections, returns and qualifications of its own members, and a majority of each shall constitute a quorum to do business; but a smaller number may adjourn from day to day, and may be authorized to compel the attendance of absent members, in such manner, and under such penalties as each House may provide." This had been interpreted that members of the House of Representatives and of the Senate could refuse to recognize the election or appointment of a new representative or senator for any reason, often political heterodoxy or criminal record. Powell v. McCormack (1969) limited the powers of the Congress to refuse to seat an elected member to when the individual does not meet the specific constitutional requirements of age, citizenship or residency. From the decision by Chief Justice Earl Warren: "Therefore, we hold that, since Adam Clayton Powell, Jr., was duly elected by the voters of the 18th Congressional District of New York and was not ineligible to serve under any provision of the Constitution, the House was without power to exclude him from its membership."The Federal Contested Elections Act of 1969 currently lays out the procedures by which each House determines contested elections.
Unseated members of Congress
- From 1869 to 1900, the House of Representatives refused to seat over 30 Southern Democratic candidates declared the winner by their states because the House Elections Committee concluded that fraud, violence, or intimidation had been used against black voters, or, in some cases, that the election statutes of the states themselves were unconstitutional. (Giles v. Harris (1903) ended the latter practice.) In some cases a new election was ordered, while in others the defeated Republican or Populist candidate was seated instead.[1][2]
- George Q. Cannon (R-Utah) was elected as the non-voting delegate for Utah Territory to the House of Representatives in 1872. He remained a duly-elected congressional delegate until 1882, when his seat was declared vacant by the enactment of the anti-Mormon Edmunds Act.
- ... a bunch more in 20th century, only one in 21st
- Roland Burris (D-Illinois), due to the Rod Blagojevich corruption charges, was initially refused a seat in the Senate in 2009. On December 30, 2008, Governor Blagojevich announced that he was naming Burris to the seat, and Illinois Secretary of State Jesse White registered the appointment in the official records of Illinois on December 31, 2008.
However, Secretary of State White declined to sign the Senate's certification form.[5] Because of this, on January 5, 2009, Secretary of the United States Senate Nancy Erickson rejected Burris's certificate of appointment to the Senate as invalid, citing Senate Rule 2 as the reason for the rejection.[6] Burris appeared in Washington at the January Congressional swearing-in ceremony on January 6 to claim his seat, but was denied entry into the Senate chambers.[7]
Following an Illinois Supreme Court ruling on January 9, 2009, White provided Burris with a certified copy of the appointment's registration, and Burris delivered that copy, bearing the State Seal, to the Secretary of the Senate.[8] On January 12, 2009, after the Secretary of the Senate announced that she and Senate Parliamentarian Alan Frumin deemed Burris's new credentials valid, Senate leaders decided to seat Burris.[9] Burris was sworn in by President of the Senate Dick Cheney on January 15, 2009.[10][11][12]
In summary: has been used successfully in the past, maybe a little harder to use now, but could still work sometimes.
We could amend the constitution. Been done before. Been done a LOT!
I can only refer you to a post by greeneyes: The US Constitution does not provide for or authorize recall...Things not specifically provided are reserved to the people-10th amendment. If that is so then there is not a rule set in the Constitution and the matter is still somewhat untested. The members of Congress are elected by the voters of the states and/or districts of their residence {except for various Democ🐀s} and I would pose the hypothesis that it is those same voters or their governors who have jurisdiction over recall of elected officials.
Since I am in way over my head right now you can log this as one of my hair-brained ideas if you like. 🙄