Sen. Patrick J. Toomey (R-Pa.), an influential conservative in the Senate, has spoken with several colleagues in recent days about possibly summoning just two witnesses to President Trump’s impeachment trial, with one called by Republicans and one by Democrats, according to three Republican officials.

Toomey has confided to GOP senators that proposing a “one-for-one” deal with Senate Democrats may be necessary at some point, particularly with pressure mounting for witnesses to be called, according to the officials, who spoke on the condition of anonymity to discuss private conversations. He has argued that such an arrangement could force Democrats to accept a Republican witness against their wishes or else risk having Republicans move ahead to acquit Trump, the officials said.

Toomey has spoken about his idea with Sen. Mitt Romney (R-Utah) and others, the officials added.

Toomey’s office declined to comment Monday.

Separately, two Senate GOP aides, who spoke on the condition of anonymity to be frank, said Romney is in touch with Toomey and generally supportive of a witness deal that he believes is fair to the GOP but has not yet signed on to any specific plan.

The proposal also came up in private conversations at Monday’s closed Senate GOP lunch, according to the officials and a Senate aide briefed on the meeting.

Toomey, who is not up for reelection until 2022, is close to Senate Majority Leader Mitch McConnell (R-Ky.). He is not close with the president or top aides in the White House.

McConnell, however, is so far discouraging Toomey’s suggestion from becoming the party’s position. Instead, he told Senate Republicans during Monday’s lunch to wait on any witness deal proposal until after Trump’s legal team is done making its defense on the Senate floor, underscoring a position he has held for weeks, the officials said.

Still, Toomey’s willingness to discuss bringing in witnesses, even under a “one-for-one” scenario, raises new questions for Trump’s team and Democrats as the trial proceeds. Will more Republicans join in and call for a contained and brief witness arrangement, such as Toomey has outlined to his colleagues? And would Senate Democrats be open to a trade after weeks of sharply criticizing Republicans for seeking witnesses they see as irrelevant to the trial?

Romney and Sen. Susan Collins (R-Maine) said early Monday that they expected other Republicans to back a push for new evidence, but they did not specify Toomey as one of the Republicans who might call for witnesses.

Those statements came after new revelations from former national security adviser John Bolton, who in his forthcoming book alleges that Trump directly tied the holdup of nearly $400 million in military aid to Ukraine to desired investigations of former vice president Joe Biden and his son Hunter.

“I think it’s increasingly likely that other Republicans will join those of us who think we should hear from John Bolton,” Romney told reporters, repeatedly calling Bolton’s testimony “relevant.” “It’s important to be able to hear from John Bolton for us to be able to make an impartial judgment.”

Collins said reports about Bolton’s unpublished manuscript “strengthen the case for witnesses and have prompted a number of conversations among my colleagues.”

Sen. Ted Cruz (R-Tex.) has taken the lead this month in calling for trading testimony from Bolton for testimony from Hunter Biden. He has called the arrangement “witness reciprocity.”

The House impeachment charges center on the allegation that Trump withheld military aid and a White House meeting to pressure Ukraine to investigate the Bidens, as well as a discredited theory that Ukraine worked with Democrats to interfere in the 2016 election.

Hunter Biden served on the board of a Ukrainian gas company, Burisma, when his father served as vice president. Trump and his personal lawyer Rudolph W. Giuliani have promoted an unfounded allegation that Biden tried to stop a corruption investigation in Ukraine to protect his son, who is no longer on Burisma’s board. Hunter Biden was not accused of wrongdoing.

Most Democrats have shot down Cruz’s suggestion — which has been echoed by other supporters of the president — as an obvious gambit to prod Democrats toward a deal that would swing the spotlight away from Trump.

“Hunter Biden is not accused of withholding $391 million of congressional authorized defense spending for one of our allies who’s under attack by Russia,” Sen. Thomas R. Carper (D-Del.) said last week. “Donald Trump is. We need to keep that in mind.”