WASHINGTON — President Biden’s legal team is laying the groundwork to defend against an expected onslaught of oversight investigations by congressional Republicans, should they take one or both chambers in the midterm elections — including preparing for the possibility of impeachment as payback for the two impeachments of President Donald J. Trump.

As part of those preparations, Mr. Biden and his White House counsel, Dana Remus, have hired Richard A. Sauber, a longtime white-collar defense lawyer who is now the top lawyer at the Department of Veterans Affairs, to oversee responses to subpoenas and other oversight efforts, according to people who spoke on the condition of anonymity to discuss internal matters.

Mr. Biden’s personal lawyer, Bob Bauer, and Ms. Remus have also been meeting for months to work out potential divisions of labor between White House lawyers and outside counsel, according to people briefed on the matter.

The arrangement is said to be aimed at respecting the limits of what taxpayer-funded lawyers should handle and ensuring that Mr. Biden’s two sets of lawyers do not mix work in a way that could inadvertently undermine executive and attorney-client privilege protecting what lawyers know from any subpoenas for their testimony or notes.

It is a routine dynamic of Washington life that when one party controls both elected branches of government, Congress goes easy on oversight. When government is divided, the opposition party is much more aggressive about wielding subpoenas and oversight hearings to try to uncover and highlight incompetence or wrongdoing by the executive branch.

But the turbulence of the Trump era and its aftermath are taking that to new levels of intensity, and some Republicans appear eager to focus on Mr. Biden and his family — particularly the foreign business dealings of his son Hunter Biden. A handful of far-right Republicans have already signed onto a flurry of impeachment resolutions.

Republicans have also signaled an intent to scrutinize various matters related to the pandemic that could reach into the White House, including the administration’s imposition of mask mandates and the extension of an evictions moratorium, both of which were later blocked in court. A particular target is Dr. Anthony S. Fauci, a top medical adviser in the Trump and Biden administrations who has become a villain to supporters of Mr. Trump.

And they have listed a series of other topics they intend to dig into, including the messy withdrawal from Afghanistan and the surge in migration across the southwestern border; another frequently mentioned target is the secretary of homeland security, Alejandro N. Mayorkas.

Late last year, Senator Ted Cruz, Republican of Texas, said on a podcast that because House Democrats had twice impeached Mr. Trump — for withholding military aid to Ukraine while pressing it to open an investigation into the Bidens, and for “incitement of insurrection” over the Jan. 6 Capitol riot — “there’ll be enormous pressure on a Republican House to begin impeachment proceedings” against Mr. Biden, “whether it’s justified or not.”

It remains to be seen whether Democrats will lose one or both chambers in the midterm elections, giving Republicans the power to open investigations and pursue subpoenas. Polls have suggested that Republicans are well positioned, but events — like the likelihood that Republican-appointed justices on the Supreme Court will soon end women’s constitutional right to abortion — could upend political dynamics before November.

Still, the party that does not control the presidency typically does well in the midterms. The decision to hire Mr. Sauber comes as Republicans crow on conservative news media and in town halls across the country about their plans to initiate ferocious oversight efforts if they return to power in 2023.

Mr. Sauber, a veteran Justice Department prosecutor, is set to start at the White House in several weeks, people familiar with the matter said. He spent years at the Robbins Russell law firm in Washington, where he specialized in representing companies and people facing congressional and other governmental investigations.

Among his clients was Susan Rice, a top official in the Obama and Biden administrations, during the Republican-led investigation into the 2012 attack in Benghazi, Libya. Another was Mary L. Schapiro, a former chairwoman of the Securities and Exchange Commission, in 2011, when she was under scrutiny by both Congress and an inspector general.

Mr. Sauber, who is known as Dick, will have the title “special counsel to the president,” which no other White House lawyer in the Biden administration has had, the people said. That reflects the elevated role his oversight portfolio is anticipated to have next year compared with what it has been under the lawyer he is succeeding, Jonathan Su, a deputy White House counsel.

“Dick is an excellent lawyer who brings decades of experience that will be a valuable asset,” Ian Sams, a White House spokesman, said in a statement, adding that “we are ensuring the White House is prepared for the issues we are facing or will face in the future.”

The secretary of veterans affairs, Denis McDonough, praised Mr. Sauber’s work at the department. “He has a deep understanding of government,” Mr. McDonough said in a statement, noting that he would be a welcome addition to the White House.

The White House has also added Mr. Sams to focus full-time on oversight matters. In the 2020 election cycle, he was a campaign spokesman for Kamala Harris, who was then a Democratic presidential candidate and is now the vice president. Mr. Sams went on to work for the Department of Health and Human Services on pandemic-related issues.

As part of the planning sessions with the White House, Mr. Bauer has also raised the possibility of hiring outside firms with special expertise to assist him, according to people briefed on the talks.

Mr. Bauer, who now teaches at New York University School of Law, was a top lawyer to Senate Democrats during the 1999 impeachment trial of President Bill Clinton. In 2011, he was the White House counsel to President Barack Obama when Republicans took over the House and began investigating matters like the botched “Fast and Furious” gun-trafficking case.

Trump-supporting Republicans have been stoking expectations that they will turn the tables next year, particularly given the level of scrutiny that House Democrats have cast on Mr. Trump and his administration: two years of congressional investigations culminating in the two impeachments, followed by the Jan. 6 committee’s inquiry into the former president’s attempts to overturn the 2020 election results.

Representative James R. Comer of Kentucky, the top Republican on the Oversight Committee, has also pledged to investigate Hunter Biden’s dealings and a cache of files that are said to have come from a laptop Mr. Biden abandoned in a repair shop. (People familiar with the matter have authenticated some emails that came from its hard drive to The New York Times, but numerous files attributed to it are circulating, and it is not clear whether all are legitimate.)

Mr. Comer said on Monday that he believed promising an inquiry into Mr. Biden’s son would bolster Republican turnout in the midterms. Voters have “suspected for a long time that Hunter Biden was a shady business guy,” he said, suggesting without evidence that both men had been “compromised” by Russian oligarchs.

The Justice Department has been examining whether Hunter Biden broke tax and foreign lobbying laws, a matter that is expected to be resolved in the coming months. Regardless of what Attorney General Merrick B. Garland decides, he is likely to face accusations from Republicans that he gave the president’s son preferential treatment.

Still, Republicans have been divided about whether it is smart to talk about impeachment already.

In April, Representative Greg Murphy, Republican of North Carolina, told Fox News that there were “plenty” of grounds to impeach Mr. Biden, citing the border crisis, Afghanistan and other ways he said the president had committed offenses “against the heart and soul of this country.” The dilemma, Mr. Murphy said, was that Ms. Harris, who would become president if Mr. Biden were removed, was worse.

A few days later, a Fox News host played that clip for Representative Kevin McCarthy of California, who is likely to become speaker if Republicans take the House, and asked whether he would move to impeach Mr. Biden. Mr. McCarthy, the minority leader, accused Democrats of using impeachment “for political reasons,” which he said Republicans would not do. Still, he vowed to hold the Biden administration accountable and follow the facts.

“We believe in the rule of law,” Mr. McCarthy said. “We’re not going to pick and choose just because somebody has power. We’re going to uphold the law. At any time, if someone breaks the law and the ramification becomes impeachment, we would move toward that. But we’re not going to use it for political purposes.”

But his comments drew immediate rebukes from a range of right-wing commentators and some lawmakers who had already endorsed impeachment resolutions. As the fallout from the Jan. 6 attack has shown — Mr. McCarthy at first said he would tell Mr. Trump to resign but then flipped to embracing him — he has a history of bending to his party’s winds.

Catie Edmondson contributed reporting.