A bipartisan group of lawmakers is warming up to the idea that Congress should insulate special counsel Robert Mueller from President Trump’s influence.

Sens. Lindsey Graham (R-S.C.) and Cory Booker (D-N.J.) introduced legislation on Thursday that would require judicial review for any attempts by the president to fire a special counsel such as Mueller. Under the bill, a panel of three judges would decide whether there was probable cause for Mueller to be fired.

Sens. Chris Coons (D-DE) and Thom Tillis (R-N.C.) filed separate legislation on Thursday that would allow a special counsel to challenge his or her termination after the fact. The case would be heard by a panel of three federal judges who would decide within 14 days whether there was probable cause for termination.

The senators said on Thursday that they would consider merging their efforts in the coming weeks.

Trump’s attacks on Mueller’s integrity and independence have spurred bipartisan backlash on Capitol Hill, where Republicans and Democrats have warned the president that it would be politically toxic if he moves to fire or discredit Mueller. The goal of both pieces of legislation, according to the senators who introduced them, is to codify the backlash that they have so far simply articulated.

“Special Counsel Mueller enjoys wide support in the Senate, and the confidence that both Republicans and Democrats have in him and in his conduct on this independent investigation, and on our level of concern that the president might take some abrupt action in the coming months, I think is reflected in the fact that you’ve seen two bills introduced in as many days,” Coons told reporters.

The dual efforts are the latest attempt by lawmakers on Capitol Hill to box the president in on Russia. This past month, a large bipartisan majority of Congress, over the objections of the White House, passed legislation that slaps new sanctions on Moscow over its election meddling and incursions into Ukraine.

“I think this is a piece of a whole series of public statements and actions by an increasingly wider range of Republican senators to push back on decisions by this White House,” Coons said. “He’s certainly encountering that; I hope he’s also discovering that.”

Trump technically can’t fire Mueller himself; that authority is left for Deputy Attorney General Rod Rosenstein, who has recently stood by his decision to appoint Mueller. But Trump has hinted he is considering that path. During an interview last month with The New York Times, Trump said Mueller would be crossing a red line if his investigation looked into his finances—a step Mueller is reportedly taking.

At the time of Trump’s statement, senators seemed resigned to being unable to preemptively shield Mueller from the threat of presidential interference.

Sen. Martin Heinrich (D-N.M.), a member of the intelligence committee, told The Daily Beast last month that Congress should stay in its “lane” and ensure that the legislative branch and the special counsel “not be connected.” A spokeswoman for Heinrich said the senator “would certainly support insulating Mueller from White House interference,” but wants to ensure that Mueller is “wholly independent from congressional influence.”

The Graham-Booker and Coons-Tillis bills represent a change in sentiment—but not one that all senators are comfortable supporting.

Sen. Susan Collins (R-ME) said the regulations already in place at the Justice Department are sufficient for ensuring that Mueller could only be fired for legitimate reasons.

“Under the Justice Department guidelines which say that the special counsel can only be removed for cause, it also requires a report to Congress already on what the justification was,” Collins told reporters. “So I think that those are likely sufficient deterrents to firing Bob Mueller.”

Senate Majority Whip John Cornyn expressed similar reservations about the new bill, saying the scenario whereby Trump tries to oust Mueller is “just a hypothetical that, frankly, I don’t think it’s necessary because I don’t think it’s going to happen.”

Trump has defied senators’ expectations before, notably when he fired former FBI Director James Comey over what the president later said was his concerns about the director’s Russia investigation. And Coons argued that both pieces of legislation introduced on Thursday are intended to guard against the possibility that Trump may ignore procedural norms again. The new proposals would “take standards that are currently regulatory and make them statutory,” he explained.

Sen. Richard Blumenthal (D-CT), who sits on the judiciary committee, predicted “overwhelming support on both sides of the aisle to provide some kind of review mechanism.”

Sen. Mark Warner (D-VA), the vice chairman of the Senate Intelligence Committee, told The Daily Beast in an interview that he supports measures to insulate Mueller from Trump’s influence, adding: “It’s frankly astonishing that Congress would have to take that kind of prophylactic action.”

—Sam Stein contributed reporting.