When the House formally censured Representative Paul Gosar, Republican of Arizona, in November 2021, it was the first time in more than a decade that the punishment had been handed out on the floor. Less than two years elapsed before the next censure — and more attempts are on the way.

No president had been impeached for 130 years before Bill Clinton faced charges by the Republican-controlled House in 1998. Donald J. Trump was then impeached twice — doubling the number of presidential impeachments. Now, many Republicans are working to impeach President Biden.

Proposals to censure lawmakers and impeach members of the Biden administration are piling up quickly in the House in an illustration of how once-solemn acts are becoming almost routine as the two parties seize on these procedures as part of their political combat. And the trend is only likely to intensify given the enmity between Republicans and Democrats over a new federal indictment brought against Mr. Trump for his efforts to overturn the 2020 election, and the G.O.P.’s desire to even the score.

The proliferation of censures and cries for impeachment is troubling to some who see it as a threat to the standing of the institution as well as diminishing the weight such punishments are supposed to carry. Censure is the congressional penalty just below expulsion.

“I think it further deteriorates everyone’s faith in the institution,” said Steve Israel, a former eight-term member of the House from New York and a top Democratic strategist. “Everything becomes political theater.”

“Both sides regarded censure as a last resort that should be insulated from political whim,” Mr. Israel said of his time in Congress. “We were careful not to rush to judgment.”

But it is a truism of the contemporary Congress that once one party does something the other sees as a breach, the aggrieved party will return fire once it gets the chance — and perhaps even take things up a notch. Tit for tat is the coin of the congressional realm.

That was evident when House Democrats twice impeached Mr. Trump despite furious G.O.P. objections that Republicans would move to return the favor at their first opportunity after regaining control of the House. And they have.

Representative Lauren Boebert, a far-right firebrand from Colorado, essentially sought to have Mr. Biden impeached in June without so much as an investigation. Representative Marjorie Taylor Greene of Georgia, another far-right Republican, had earlier filed her own articles of impeachment against the president.

After sidestepping Ms. Boebert, House Republicans are now conducting what they characterize as an “inquiry” into a potential impeachment, one that is likely to gain steam in the G.O.P. backlash to the new indictment. And it is not just Mr. Biden in their sights but other administration officials including the homeland security secretary, Alejandro Mayorkas, and Attorney General Merrick B. Garland, even though there is no chance any would be convicted in the Democratic-controlled Senate.

Lawmakers across Capitol Hill saw this coming.

“I said two years ago, when we had not one but two impeachments, that once we go down this path it incentivizes the other side to do the same thing,” said Senator Mitch McConnell, Republican of Kentucky and the minority leader.

“Impeachment ought to be rare,” he said, adding, “This is not good for the country.”

As for censures, Speaker Kevin McCarthy embraced meting out that penalty to Representative Adam B. Schiff, the California Democrat and former Intelligence Committee chairman who led the first impeachment prosecution of Mr. Trump.

The censure, brought forward by Representative Anna Paulina Luna of Florida, a strong supporter of Mr. Trump, accused Mr. Schiff of lying and spreading distortions in his investigation of the president. Some Republicans were clearly uncomfortable with the idea of censuring Mr. Schiff, and the move failed on its first attempt. But after Ms. Luna dropped a proposed $16 million fine from her resolution, Republicans pushed through the censure on a party-line vote in June.

Far from hanging his head in ignominy, Mr. Schiff said he welcomed the vote as a badge of honor that proved he was effective. It provided a fund-raising boost for his campaign for a Senate seat and should he ultimately win, it will probably be seen as a turning point in his effort to succeed Senator Dianne Feinstein, the ailing California Democrat.

Since that censure, multiple other resolutions have been introduced, including a Republican one to censure Representative Bennie Thompson, the Mississippi Democrat who was the chairman of the special committee that investigated the Jan. 6, 2021, attack. Another Republican-sponsored effort targets Representative Pramila Jayapal, Democrat of Washington, for referring to Israel as a “racist state” — a statement she has withdrawn.

A newly introduced Democratic censure resolution takes aim at Ms. Greene for “hateful rhetoric” and a series of other acts, including showing sexually explicit photos of Hunter Biden, the president’s son, at a recent hearing examining his business ventures.

Representative Becca Balint, a first-term Democrat from Vermont and the resolution’s author, said she was initially reluctant to introduce the censure resolution against Ms. Greene but ultimately felt she had to act upon arriving in Congress and finding the atmosphere so politically poisonous.

“At what point do we try to have some accountability?” she asked.

Ms. Greene dismissed the censure attempt as a fund-raising ploy.

Democrats are also pressing to censure Representative George Santos, Republican of New York, for blatantly lying to voters about his life story.

The rise in censure attempts is marked. Before Mr. Gosar was censured in 2021 for circulating a video on social media that depicted a violent attack against a Democratic congresswoman, the previous one was the 2010 censure of Charles B. Rangel, Democrat of New York and a once-powerful committee chairman. He was the subject of a bipartisan vote to reprimand him for financial misconduct after a lengthy ethics investigation. Two censures preceding his came in 1983 for sexual misconduct with House pages. Earlier censures also followed such serious charges as bribery, fraud and assaults on colleagues.

But the standards for both censure and impeachment are changing, and some lawmakers see it as a step in the wrong direction.

“I just think we need to try to work out our political differences and not use tools like impeachment to try to redress our grievances,” said Senator John Cornyn, Republican of Texas. “I don’t think it is a healthy sign for us to be resorting to the ultimate weapon.”

“But democracy is messy,” he added, “and we are demonstrating that every day.”