WASHINGTON — Another senior member of President Trump’s legal team is stepping down, the latest high-level turmoil as the White House grapples with special counsel Robert S. Mueller III’s efforts to interview the president — and to subpoena him if necessary.

The shake-up on Wednesday was seen as another sign that Trump is seeking a more combative approach to the Russia investigation, which has clouded his presidency from the start and led to criminal charges against several former aides so far.

It also may signal that Trump will refuse to submit to an interview or will fight a grand jury subpoena, setting the stage for a constitutional battle over his executive powers. The legal question of whether a president can be required to answer questions in a criminal case has never been tested.

The confrontation looms as Ty Cobb, the White House lawyer who advocated for cooperating with Mueller’s prosecutors, including for Trump to submit to an interview, prepares to exit this month and be replaced by Emmet Flood.

Flood helped represent President Clinton at his Senate impeachment trial in January 1999. Clinton was acquitted on charges of perjury and obstruction of justice.

In a statement, Sarah Huckabee Sanders, the White House press secretary, said Flood would represent the president and the administration “against the Russia witch hunt,” using the harsh rhetoric that Trump deploys almost daily but Cobb avoided.

Trump’s thin stable of lawyers has undergone considerable turnover since the Justice Department named Mueller as special counsel last May. Mueller is investigating whether any Trump aides cooperated with Russian efforts to manipulate the 2016 election, and whether Trump obstructed justice by trying to block or influence the inquiry.

Trump last month hired former New York Mayor Rudolph W. Giuliani, a onetime federal prosecutor, to replace John Dowd, a veteran white-collar defense attorney who was the president’s lead lawyer before resigning in March. Giuliani reportedly has met with Mueller and is seeking to negotiate limits to any potential testimony by Trump.

The first test of Trump’s increasingly bellicose stance will likely come as Mueller continues to push for a presidential interview. In a testy meeting in early March, the former FBI director told Trump’s lawyers that he could issue a subpoena for the president to testify before a grand jury, according to the Washington Post.

Trump seemed to confirm details of the March meeting in a tweet Wednesday evening, sharing a comment that Dowd had reportedly made to prosecutors — “This isn’t some game. You are screwing with the work of the president of the United States.”

The possibility of a subpoena has raised the stakes for Trump, who has publicly said he is eager to sit down with prosecutors even though his advisors believe it would be a perilous encounter given the president’s routine use of exaggeration, hyperbole and outright falsehoods.

With Cobb’s departure, “the number of people who think the president should talk to Mueller has gotten to zero,” said a source familiar with the legal team who declined to speak publicly about their deliberations.

If Trump resists a grand jury subpoena, the dispute could rocket to the top of the U.S. Supreme Court’s docket, setting the stage for an unprecedented showdown between the executive and judicial branches.

Several previous White House episodes are relevant, although none shows clearly how the justices might rule.

In July 1998, independent counsel Kenneth W. Starr issued the first subpoena to a sitting president to compel Clinton to testify to the Monica S. Lewinsky grand jury. Several weeks later, Clinton agreed to submit to four hours of questioning by prosecutors at the White House after Starr withdrew the subpoena.

In June 1974, during the Watergate scandal, the Supreme Court voted unanimously to force President Nixon to give a special prosecutor secretly recorded audiotapes of the president’s conversations.

The release of the Oval Office tapes helped turn public opinion against Nixon, and he resigned two months later. But the decision did not address the question of whether Nixon could be required to testify.

Senior members of Congress have warned Trump not to try to fire Mueller, warning it could lead to a constitutional showdown. But a Trump refusal to submit to a special counsel interview or honor a subpoena could be a fast track to a similar result.

“There’s a potential for a constitutional crisis right around the corner in all of these things,” said Randall D. Eliason, a former federal prosecutor in Washington who teaches white-collar criminal law at George Washington University.

Many legal experts say Trump could not legally refuse a grand jury subpoena.

“I could see it going back to the Supreme Court,” said John Yoo, a senior Justice Department lawyer during President George W. Bush’s first term, who now teaches law at UC Berkeley. “But I don’t see how Trump could win.”

Paul Rosenzweig, who worked with Starr in the Clinton investigation, said Trump could delay his testimony by fighting a subpoena, but ultimately he would fail in the courts.

“It would not succeed in the long run,” he said.

Not even Alan Dershowitz, an emeritus professor at Harvard Law School who has been among Trump’s highest-profile defenders, believes the president could reject a subpoena out of hand. He said Trump may be able to avoid certain lines of questioning involving, for example, the firing of James B. Comey as FBI director, because the president’s power to dismiss members of the executive branch is undisputed.

If Trump chooses to litigate, Dershowitz said, “I think he’d win on some areas and lose on some areas.”

Mueller appears to have anticipated a high-stakes legal clash. His team includes Michael Dreeben, a highly respected deputy solicitor general who two years ago earned the rare distinction of arguing more than 100 cases before the Supreme Court.

At least part of the scope of Mueller’s investigation was revealed this week when the New York Times obtained a list of about four dozen likely questions for Trump that was compiled by the president’s lawyers after they spoke to Mueller’s team in March.

The list includes several inquiries about what Trump knew about Russian interference in the election and why he decided to fire Comey. It’s unclear whether Mueller’s interests have changed or expanded since Trump’s lawyers made the list.

Trump apparently had constitutional issues, and the list, on his mind early Wednesday.

“The questions are an intrusion into the President’s Article 2 powers under the Constitution to fire any Executive Branch Employee,” he tweeted, citing comments from Joseph diGenova, a former federal prosecutor who almost joined his legal team.

“There was no Collusion (it is a Hoax) and there is no Obstruction of Justice (that is a setup & trap),” Trump added.

Cobb, the outgoing lawyer, was hired last July as the White House attorney for the Russia investigation. In an effort to help Mueller reach a speedy conclusion, he urged full compliance with prosecutors’ requests, arranged interviews with White House officials and turned over reams of documents.

He maintained that stance Wednesday, telling ABC News that an interview with Mueller wasn’t off the table. He also said the special counsel’s office didn’t leak the list of questions for Trump, a disclosure the president had called “so disgraceful.”

Cobb’s legal strategy came under fire from Trump’s more combative allies, such as former White House strategist Stephen K. Bannon and independent operative Roger Stone. Cobb also lost standing in the Oval Office as his frequent predictions that the Russia inquiry was nearly over failed to come to pass.

“Ty Cobb was a mistake from the beginning, totally incompetent and in over his head,” Bannon told the Los Angeles Times on Wednesday.

“Cobb argued that cooperation would lead to some sort of special relationship with Mueller, but he failed to realize that there never would be or could be a special relationship with a by-the-book guy like Mueller,” he added.

Cobb said in a statement that he had discussed his retirement for a few weeks and was “glad the president persuaded Emmet to carry the torch forward.”

Flood, a graduate of Yale Law School and former clerk for the late Supreme Court Justice Antonin Scalia, is best known for his work on Clinton’s legal team in the impeachment proceedings. Clinton was impeached by the Republican-controlled House in December 1998 but was acquitted by the Democratic-controlled Senate less than two months later.

Flood also served for two years in the White House counsel’s office under Bush. Since then he has worked at Williams & Connolly, a prominent litigation firm that handles civil, criminal and administrative cases.

Lanny J. Davis, who also represented Clinton, said Flood’s new job would be a challenge because Trump is a famously difficult client.

“No matter how good your legal instincts are,” Davis said, “your effectiveness is only as good as President Trump’s ability to face reality and tell you all of the truth.”

chris.megerian @latimes.com

Times staff writer Noah Bierman in Washington contributed to this report.