While Democrats are preparing to wage war against President Trump if they win control of the House next year, both sides have also begun to look for areas where they could cooperate, eager to show voters they can deliver results even in a divided government.

House Minority Leader Nancy Pelosi (D-Calif.) has in recent days begun laying out the case for how Democrats could vigorously investigate the Trump administration but also compromise with the president when their policy priorities align.

“We worked with George Bush,” she said Monday at an event hosted by CNN. “I disagreed with him on the war in Iraq vehemently. But we worked with him on so many other subjects, passed the biggest energy bill in the history of the country, passed many pieces of legislation.”

The White House is also sensing a political benefit in finding areas of agreement, and top administration officials have reached out to key Democrats to see where the two opposing sides could collaborate. Shahira Knight, the White House’s director of legislative affairs, recently had a private sit-down with Rep. Peter A. DeFazio (D-Ore.), who would be the Democrats’ point person on infrastructure legislation should that surface at the top of the legislative agenda in 2019.

DeFazio explained his three-pronged infrastructure proposal, and while Knight did not give direct feedback on his plan, DeFazio said, she relayed an encouraging tone from Trump on potential infrastructure efforts next year.

“She is convinced the president wants to do something real and realizes it’s going to require real money,” DeFazio said. “This guy, he was a developer. He understands . . . what happens when you build things. You put people to work, you provide jobs.”

The tension between investigating Trump’s administration while also searching for common legislative ground would be a continual balancing act for Democrats should they win control of the House, which has been in Republican hands since 2011.

Pelosi and other Democratic leaders have made clear that much of their efforts would be dedicated to conducting oversight of Cabinet officials and agencies they argue have demonstrated little regard for ethics rules and safeguarding taxpayer dollars.

To that end, Democratic aides in recent days have sought advice from former congressman Henry A. Waxman (D-Calif.), who led the party’s last full-fledged oversight effort after Democrats took over the House in 2006. And Democrats are reviewing letters they have sent to the administration that have gone ignored while sketching out what their investigative targets will be if they gain subpoena power.

“What we will do is exercise oversight, which is the responsibility of the Congress of the United States, exercise oversight over the agencies of government, which this administration has completely walked away from,” Pelosi said at Monday‘s event.

Behind Pelosi is a group of chairmen-in-waiting hungry to extract answers from an administration that Democrats say has stonewalled them and has been protected by House Republicans unwilling to investigate a president of their own party.

“I think every ranking member, their staffs are looking at this,” said Rep. Raúl M. Grijalva (D-Ariz.), who is poised to become chairman of the Natural Resources Committee if Democrats win control of the House. “If there’s a new majority . . . we can’t waste time. We have to hit the ground running from Day One.”

Still, Democrats are aware that even if they win the House with a significant mandate from voters, they risk overreaching if they engulf the administration with a number of probes — a message echoed by veterans of congressional oversight efforts.

A dozen years ago, Waxman prioritized his oversight targets of waste, fraud and abuse of taxpayer dollars within the George W. Bush administration and conducted extensive investigations on the war in Iraq. He stressed that congressional probes should be “approached in a straightforward, honest way” and that the investigative powers “should not be abused.”

“Any investigation that looks like it’s just a political witch hunt or for partisan purposes will not be credible,” said Waxman, who retired from Congress in 2015. “If subpoenas are issued wildly and it’s not clear what they’re getting at, I think the Democrats would open themselves to attacks from President Trump.”

Waxman, along with Phil Schiliro and Phil Barnett, two former top House Oversight Committee aides, have been informally advising House Democrats on how they should approach investigations of the Trump administration. 

Schiliro noted that after he began working on investigations under Waxman in the early 1980s — except for when Rep. Dan Burton (R-Ind.) led the committee between 1997 and 2003 and issued more than 1,000 subpoenas — about only 10 subpoenas were used, by Waxman. “There’s a reason for that,” Schiliro said. “Subpoenas are a powerful, intrusive mechanism, and they should only be used as a last resort.”

Democrats will also face the question of whether to try to impeach Trump — something that could also look like an overreach to voters. Trump has been warning that Democrats will try to remove him from office if they seize control of Congress. Pelosi has tried to downplay the idea, while some of the more liberal members in her caucus continue to tout the possibility.

If Democrats win the majority, an immediate priority will be staffing up quickly. Democrats on the Oversight Committee, which has the broadest investigative jurisdiction, will get twice the budget and staff they have now if they gain power. 

House Democrats have received résumés already from prospective staffers, with many interested in oversight duties, according to one senior Democratic official who like others interviewed spoke on the condition of anonymity to candidly discuss party strategy on oversight.

Allies of the White House have been concerned for weeks that the administration is not equipped to respond to the coming avalanche of investigations. 

The White House counsel’s office, which would run point on congressional inquiries, is in a transitional period with counsel Donald McGahn leaving the administration this week and many other vacancies in the office remaining unfilled. Emmet Flood has taken over in the interim until incoming White House counsel Pat Cipollone joins the staff. 

Trump has downplayed the threat posed by the looming potential clash between his administration and Democratic-controlled House. 

“I think I’ll handle it very well,” Trump said in an Associated Press interview last week when asked how he would deal with Democratic investigations, referencing ongoing Russia probes. “I’m handling already. We have a witch hunt now going on, and I handle it very well, and there was no collusion. Everyone knows it.”

The list of potential investigative targets for Democrats is already long. 

Rep. Adam Smith (D-Wash.), the top Democrat on the Armed Services Committee, would have broad latitude to investigate matters involving the military, including the administration’s policies on civilian casualties during conflict and plans to house migrant children on military bases. 

The House Veterans’ Affairs Committee would be sure to probe the alleged “shadow VA” involving three members of Trump’s private Mar-a-Lago resort in Palm Beach, Fla., who have reportedly been steering major veteran policy from outside the agency. Grijalva wants to look into conflict-of-interest issues at the Interior Department and at climate-change matters from his perch on the Natural Resources Committee. 

The House Homeland Security Committee, where Rep. Bennie Thompson (D-Miss.) is the lead Democrat, would probably delve into oversight of the administration’s immigration and border security policies, election security and the government’s response to Hurricane Maria, according to another Democratic aide. 

Rep. Elijah E. Cummings (D-Md.), in line to lead the Oversight Committee, has begun dividing his investigative priorities into two main areas — probing ethical issues, such as Trump’s business dealings and questions about the use of taxpayer money that have dogged top Cabinet officials, and examining policies that directly affect constituents, such as the cost of prescription drugs and access to voting.

“If I become chairman, I will not be looking to make headlines,” Cummings said in a statement to The Washington Post. “I see my role as defending the truth. This is not normal. Hopefully Democrats can steer us back to some normalcy.” Supreme Court Justice Brett M. Kavanaugh, who was confirmed this month after grueling and controversial proceedings that were roiled by allegations of sexual misconduct, would also be a ripe Democratic target.

Pelosi has said she will file a document request under the Freedom of Information Act for the FBI’s background report into Kavanaugh and related records. Rep. Jerrold Nadler (D-N.Y.), the top Democrat on the House Judiciary Committee, has also already discussed his plans to launch a probe into the FBI’s background investigation into Kavanaugh, as well as accusations that Kavanaugh was not forthcoming to the Senate in his hours of testimony. 

While in the minority, Democrats have already developed a way to streamline coordination among key committees on oversight of the Trump administration — an apparatus that one Democratic official said will “enable us to hit the ground running on Day One” if the party takes back power.

But some top party priorities such as securing Trump’s tax returns are already posing complications. Democrats expect the Trump administration to deny any request from Rep. Richard E. Neal (D-Mass.), who is in line to take over the powerful tax-writing House Ways and Means Committee, to obtain Trump’s tax returns from the Internal Revenue Service. House Democrats then would have to determine whether to sue for the returns — a far-from-settled decision that could launch a months-long legal fight. 

What to do with the returns is also far from simple. One option would be for Democrats to ask for the Joint Committee on Taxation to audit them. If Democrats want to release them publicly, that would require a closed-door committee vote. “We’re still trying to wrap our head around this process,” another senior House Democratic aide said. 

Mike DeBonis contributed to this report.