House Democrats are quietly working to keep a simmering turf war from erupting during their first blockbuster hearing with President Trump’s onetime top associate — an early test of whether they can pursue complex and crisscrossing probes of the administration without turning on each other.

As the House Oversight and Intelligence committees prepare to interview Trump’s former personal attorney Michael Cohen this week, several Oversight Committee members are balking at terms the panel chairmen agreed to, dictating that all Russia matters will be addressed by the Intelligence Committee alone. The disagreement flared up during a late-night strategy session Monday, when some senior Oversight Committee lawmakers said they wanted to ask Cohen about Trump Organization connections with Russian oligarchs and Russia finances.

The Intelligence Committee is scheduled to question Cohen behind closed doors on Thursday, a day after his high-profile public testimony before the Oversight Committee on Wednesday.

The dispute highlights the challenges eager House Democrats face as they delve deep into investigations of the president, the first since the party captured control of the House last November. Several committees have jurisdiction over controversies that have plagued the administration — and each one wants a turn in the spotlight.

But Democratic leaders have sought to avoid such overlap and streamline their efforts, because of fears that multiple committees investigating the same issues will make the party seem overzealous and too political. There are also logistical concerns that overlapping document requests and invitations for repetitive testimony could slow the process.

“We shouldn’t be tripping over each other,” said Rep. Jackie Speier (D-Calif.), a member of both committees.

In the case of Cohen, there is another complicating factor: desire among Democrats not to impede what remains of special counsel Robert S. Mueller III’s probe into whether the Trump campaign colluded with Russia in the 2016 election. Intelligence Committee members argue that’s the main reason Russia matters should be addressed only in the confines of their closed-door session.

How the Oversight and Intelligence committees handle the potential jurisdictional clash this week may be the first test of how well House Democrats can cooperate in the spotlight, but it won’t be the last. Several committees have expressed interest in investigating the same topics falling under their overlapping jurisdictions.

Speier, for instance, noted that the House Judiciary Committee has been seeking answers from Trump officials on the administration’s controversial family separation policy at the U.S.-Mexico border. But on Tuesday, Oversight Committee Democrats subpoenaed documents related to the same policy.  

Additionally, House Foreign Affairs Committee Chairman Eliot L. Engel (D-N.Y.) said he wanted to investigate Trump’s one-on-one meeting with Russian President Vladimir Putin, potentially even calling Trump’s interpreter to testify. Intelligence Committee Chairman Adam B. Schiff (D-Calif.) is also looking at that angle. 

“We’re not going to step on each other’s toes,” Engel said. “We’re talking every day. We’re figuring out the best way. We’re not getting in the way of each other. Believe me, there is plenty there for everybody.”

Cohen’s testimony on Wednesday is expected to dominate Washington as the former Trump fixer and close business associate accuses the president of “lies, racism and cheating,” according to a person familiar with the matter.

The White House and GOP allies on the Hill have sought to discredit Cohen as a liar who can’t be trusted. In a statement Tuesday, White House press secretary Sarah Sanders called Cohen a “disgraced felon” and said that “it’s laughable that anyone would take a convicted liar like Cohen at his word.” 

Trump has said publicly that he is not concerned about Cohen’s testimony, but privately his advisers said that they are preparing for him to delve into uncomfortable issues for Trump, including hush payments to women. White House officials are frustrated by the split-screen spectacle expected on Wednesday, when Cohen’s testimony is scheduled to begin just after Trump finishes dinner in Hanoi with North Korean leader Kim Jong Un and just before the two leaders meet for a day of high-stakes nuclear arms negotiations. 

“It’s unfortunate this is happening now,” said one White House official, who spoke on the condition anonymity to discuss the Cohen hearing.

Rep. Elijah E. Cummings (D-Md.), chairman of the Oversight Committee, and the Intelligence Committee’s Schiff worked out an agreement in recent days on how to divide up Cohen’s questioning. Under the terms, Oversight Committee members would stick to questions about the president’s business interests, potential conflicts of interest, and hush payments during the 2016 campaign to women alleging affairs with the president. Intelligence Committee members will focus on Russia and potential financial leverage other foreign actors may hold over Trump and those close to him.

But some Oversight Committee Democrats are arguing that the public has a right to hear why Cohen lied to Congress about plans to build a Trump Tower in Moscow during the 2016 election. And since the Oversight Committee’s hearing is the only public forum for Cohen’s testimony before he goes to prison, these members and aides believe it should be fair game.

During the late-night House Oversight Committee meeting, senior panel members Gerald E. Connolly (D-Va.) and Stephen F. Lynch (D-Mass.) expressed the same sentiment. They asked why the committee would agree to these terms with the Intelligence Committee. And they ticked off a list of Russia-related questions they wanted to explore in the hearing.

Lynch, one of the Oversight Committee Democrats unhappy with the scope rules, said the agreement effectively means House Democrats will “wall off a whole segment [of Cohen’s story] that is of extremely and keen interest to the American people.”

“When you have a friendly witness you get them to tell their story, so by unofficially compartmentalizing the testimonial process, he can’t do that,” said Lynch, who added that it “just does not work well mechanically.” Lynch said he will try to follow the rules but argued that “we’re trying to bring some transparency to the process, but while we’re doing that we’re also not having a full and open and honest discussion.”

Asked about his pushback over the scope of the hearing, Connolly played down the disagreement on Tuesday.

“We have broad jurisdiction over everything,” on the Oversight Committee, Connolly said, “but that means that we also overlap in jurisdiction with somebody — always. And we always want to be respectful of that. We don’t want to trample on other people’s interest. . . . So, engagement is important here and you do the best you can.” 

Connolly and Lynch are far from the only Oversight Committee members who want to explore the Trump Organization’s connections with Russia. Rep. Jamie B. Raskin (D-Md.) said he and his colleagues “will have to” ask about Russia in some capacity because “the corporate practices of the Trump Organization are of great interest to us, and there are all these emolument clause violations taking place because of entanglements with foreign governments.”  

Asked about how that overlaps with what the Intelligence Committee was investigating, Raskin added: “It’s a delicate allocation of labor between the Intelligence Committee and the Oversight Committee. Intelligence certainly is going to be the one focused on the active-measure intelligence operation conducted by the Russians against us, but it obviously blends into the domestic politics here.” 

Another House Democrat was more blunt but spoke on the condition of anonymity to speak frankly: “Who is it that makes up these rules? . . . I do not believe that members of the Oversight Committee are going to be bound by the rules of another committee.”

But Schiff and other Democrats have stressed that the limits are in place for a reason — and point out that even if members want to pepper Cohen with Russia questions, he may not answer them in the open forum because of the ongoing investigation.

“We’ve had to juggle a number of equities . . . and do our best to accommodate the interests and concerns of the special counsel’s office and the Southern District of New York,” Schiff said in an interview. “My understanding is that whether questions are posed or not posed that go beyond what the chairman [Cummings] has said, that the witness will only be responding to things within the scoping document.”

There are also pragmatic reasons that party leaders want Schiff at the helm of all things Russia. They’ve cited the importance of exploiting each committee’s investigative strengths, and Schiff’s committee has the staff and the clearance to view and investigate more sensitive intelligence matters, including counterintelligence and money laundering, that some other panels lack the expertise to fully explore.

Additionally, the Intelligence Committees in the Senate and House — the committees to which Cohen pleaded guilty to lying — had long had an interest in bringing him back to clear up the record, particularly concerning the timeline of the Trump Tower project the president sought to build in Moscow.

Since Cohen adviser Lanny Davis had a close relationship with Cummings, the two parties agreed to schedule his appearance just after Democrats took the House. But when Cummings announced the hearing in January, it caught other panels by surprise, according to several people on Capitol Hill who had expected he would appear before the intelligence panel.

Schiff immediately said he would to schedule Cohen for closed-door testimony alongside his Oversight Committee appearance, so he could address the lies he confessed to telling the panel in 2017, as well as other topics too sensitive for a public hearing. When Cohen canceled his Oversight Committee testimony citing fears about his safety, several members of that committee were upset about the fact that Schiff had seemingly secured closed-door testimony, worried that they would miss their chance to question him.

Eventually Cohen rescheduled every appearance he had planned before congressional panels — including one with the Senate Intelligence Committee — to this week.

Though the panels swiftly agreed to chalk up the experience to a coordination mistake, the episode has served as a reminder to Democrats of how they don’t want to appear to be doing business.

Since the beginning of the year, staffers from the approximately half-dozen panels involved in investigations of Trump are meeting almost weekly. The panel chairs have also joined forces to release several joint letters demanding responses from the administration, insisting that new Attorney General William P. Barr release the full special counsel’s report and pushing Treasury Secretary Steven Mnuchin to halt a planned rollback of sanctions affecting a Russian oligarch close to Putin. 

But when letters and investigations get to the point of public hearings with critical witnesses, committee staffers and chairs are limited in their power to enforce cooperative discipline, and the potential for tension — such as that surrounding the Cohen questions — remains.

I don’t want to speculate about what might or might not happen,” Schiff said of Wednesday’s Oversight Committee hearing. “All I can tell you is that the two committees have reached agreement on it, which we consider a good sign.”

Philip Rucker in Hanoi contributed to this report.