Washington (CNN) The House Judiciary and Intelligence committees could bring additional articles of impeachment against President Donald Trump, House general counsel Douglas Letter said when asked point-blank by a judge on Friday at the federal appeals court in Washington.

The responses, pushed by Judge Thomas Griffith at the US Court of Appeals for the DC Circuit, illustrate why the House believes the Mueller investigation is still relevant during this era of impeachment.

"There've been two articles of impeachment that have been acted upon. Are you here to say that there may be a third?" Griffith asked.

"There might, yeah, absolutely," Letter responded as Griffith continued his line of questioning.

"The House Judiciary Committee has not finished its work on impeachment," Griffith offered.

"Nor has the Intelligence Committee," Letter said.

While the committees continue to look into Mueller's work, details from the criminal investigations in the Russia probe, which the House currently cannot see because they are protected under grand jury secrecy rules, could be used during the upcoming Senate impeachment trial, Letter said.

The details from Mueller could flesh out Senate proceedings over the President's solicitations of foreign government political help, or add to his alleged obstruction of Congress, Letter said. Separately, Mueller's findings could bolster a case for the House to make that Trump tried to obstruct the Russia investigation into him and his campaign.

"There's nothing more important than determining if the President of the United States should remain President of the United States," Letter said.

Before Letter spoke to the panel of three judges, another House lawyer, Megan Barbero, fielded Griffith's questions over the House's unfulfilled subpoena of former White House counsel Don McGahn . The judge pressed her to say what was in the cards related to Mueller's obstruction of justice investigation, for which McGahn was a key witness. Were more articles of impeachment on the table, he asked her.

"You have authority to say this from the speaker of the House?" the judge asked.

Barbero, representing the Judiciary Committee, dodged a direct reply. Instead, she said Congress could use McGahn's testimony to inform the impeachment trial, especially regarding Trump's alleged obstruction of Congress.

But more than an hour later, Letter reiterated that his team in court could represent House Speaker Nancy Pelosi's positions.

The exchanges came in a doubleheader of appeals court proceedings about House committees' attempts to gather more information unearthed by the Mueller investigation. The House had sued shortly after Mueller finished his work because it couldn't review some redacted details in his report related to grand jury proceedings, and because the White House had blocked McGahn from testifying about any attempts by the President to obstruct justice.

The McGahn and Mueller grand jury cases, taken together, are significant court challenges that could affect impeachment proceedings and the standoff between the US House and the administration.

Though one Democratic-appointed judge hearing the cases on Friday seemed deeply skeptical of the Justice Department's arguments, the other judges, including Griffith, were harder to read.

The judges on the DC Circuit Court of Appeals panels on Friday asked multiple questions about the state of play in impeachment proceedings, pushing Trump administration attorneys on the President's blanket refusal to comply with congressional subpoenas.

The three hours covered a dense range of legal questions, including whether courts can resolve political disputes between Congress and the executive branch.

Hashim Mooppan from the Justice Department, which is defending McGahn, warned the appeals court to stay out of the House-White House fight, at the risk of politicizing the court. "You can be assured the opinion this court enters will be waived on the floor of the Senate by one side or another," he told the three appellate judges.

"Has there ever been an instance of such a broad-scale defiance?" Griffith asked, about the Trump administration's wide assertion that its top officials would not comply with congressional subpoenas. "Has that ever happened before? No, it hasn't."

As Mooppan argued that the courts shouldn't be involved and Congress could find ways to work out a political solution with the White House, Judge Judith Rogers, leaning far back in her chair, cut in, "Takes two!"

Mooppan also said Congress could retaliate against the White House by passing legislation or through impeachment.

At another point, Griffith asked if the House really needed McGahn for its current impeachment proceeding, which focuses on the President's solicitations of Ukraine after McGahn left the West Wing. "You're here because of impeachment," he said.

Rao's extraordinary hypothetical

Throughout the arguments, the judges circled back to questions over the limitations of the power of the courts in fights between Congress and the executive branch.

Judge Neomi Rao led Letter into an extraordinary hypothetical: What if the appellate court says the House can view Mueller grand jury details for its impeachment proceedings, but Attorney General William Barr refuses to turn over the materials to Congress?

Letter said the House, in that case, would have to send its sergeant-of-arms to the Justice Department to pick up the documents -- and in that sort of "astonishing" situation could be like a gun battle between Barr's FBI detail and House officials.

"Instead, we go to court! Everybody has recognized that. We go to court," Letter said, admitting he hadn't thought through the possibility Rao raised.

Rao clarified that she wasn't asking about what Barr would do, but whether the court itself has the ability to force the Justice Department to release the secret information a grand jury collected and Mueller cited in his final report.

The fight in lower courts

So far, federal trial-level judges have given House Democrats the greenlight for access to those Mueller documents and said McGahn must at least show up for testimony under subpoena. But the House still has yet to review confidential testimony and details collected during the Mueller investigation, or to have the opportunity to question McGahn, perhaps the top witness to Mueller on Trump's attempts to fire special counsel Mueller and allegedly obstruct the Russia investigation.

Judges so far have pointed out how closely the court fights reflect upon current proceedings about Trump.

"Presidents are not kings," DC District Judge Ketanji Brown Jackson wrote in her November opinion that said McGahn must testify and the White House couldn't block congressional subpoenas for its former top officials. An appellate ruling about McGahn could quickly become the determinate in how much the House or Senate can access top Trump officials the White House has blocked from testimony during impeachment. The White House has used the same reasoning to block McGahn as it's used to stop other witness from speaking to Congress about Trump's approach to Ukraine.

Separately, Chief Judge Beryl Howell of the DC District Court, who oversaw Mueller's grand jury, wrote in her opinion that the House should get access to details Mueller collected through a grand jury so Congress could continue investigating the President. Howell's opinion was an early and important legal endorsement of the House impeachment proceedings, even before the full House voted to authorize the inquiry.

"Congress need not redo the nearly two years of effort spent on the Special Counsel's investigation," Howell wrote in October. The House Judiciary Committee "needs the grand jury material" Mueller collected, she added in her opinion, "to resolve questions -- including the ultimate question whether the President committed an impeachable offense -- that the Special Counsel simply left unanswered."

In a previous court argument related to the Mueller grand jury case, the House attorneys told judges the Democrats could still pursue impeaching the President for other reasons, even after the current impeachment regarding Ukraine has passed.

Any decisions in the cases, made by panels of three appellate judges for each case, are likely to face further appeals tests, including potentially before the Supreme Court.

Griffith is an appointee of George W. Bush and Rogers was nominated by Bill Clinton. The pair of judges heard both cases on Friday. Rao, a Trump appointee, rounded out the panel on the grand jury secrets case, while Judge Karen Henderson, a George H.W. Bush appointee, was the third judge to hear the McGahn arguments.

This story has been updated with additional developments.