Senate Republicans are privately debating whether they should use an impeachment trial of President Trump to scrutinize former vice president Joe Biden and his son Hunter as some Trump allies push to call them as witnesses while others dismiss the suggestion as a risky political ploy.

The ongoing discussions are a revealing glimpse into the fault lines in the GOP ahead of a possible trial of Trump in the upper chamber, where there are varying appetites among Senate Republicans for the type of political combat relished by the president and his most hardcore defenders.

Among a group of Trump’s allies inside and outside Congress, there is intense and growing interest in countering the House Democrats’ impeachment inquiry with their own scrutiny of Hunter Biden’s overseas business dealings in Ukraine and China. Because his father was vice president at the time, these allies believe it could be a way of explaining why Trump pressed Ukrainian President Volodymyr Zelensky in a July 25 phone call to “look into” the Bidens, who have denied any wrongdoing.

That effort gained steam on Capitol Hill last week at a private lunch where Republican Sens. Rand Paul (Ky.) and John N. Kennedy (La.) raised the idea of summoning Hunter Biden, according to two people familiar with the exchange who, like others in this article, spoke on the condition of anonymity because they were not authorized to speak publicly. Paul took his private push public at a campaign rally with the president Monday night in Kentucky.

“I say this to my fellow colleagues in Congress, to every Republican in Washington: step up and subpoena Hunter Biden and subpoena the whistleblower!” Paul told the crowd, also referring to the unnamed intelligence official who first raised alarms about the president’s Ukraine conduct.

Yet many Senate Republicans have reservations about such a strategy, fearing it would look overtly political and that it may not be appropriate, or even possible, to include such witnesses in an impeachment trial.

“I think that’s a sideshow,” Sen. John Cornyn (R-Tex.) said of calling in Hunter Biden. “[Impeachment] is a very solemn and serious constitutional process, and I just think that whatever the House decides to vote on . . . that’s what we ought to consider and not make this any more of a reality show than it’s likely to become.”

The back-and-forth sets up a looming clash between Trump loyalists and more traditional-minded Senate Republicans who are uncomfortable with Trump’s no-holds-barred tactics in defending himself. Many Senate Republicans, for example, also have little interest in outing the whistleblower, even as the president and his allies have argued the person should be named and targeted with a subpoena.

But Paul’s position on the Bidens has been echoed by Trump’s loyalists in the conservative media, ramping up the pressure campaign on Senate Republicans to be more aggressive in defending the president.

“The Bidens have to be called,” former White House chief strategist Stephen K. Bannon said Sunday on Fox News. “Joe Biden is a hand grenade and Hunter Biden is the pin. And when that pin gets pulled, the shrapnel is going to blow back all over the Democratic establishment,”

At the center of the deliberations is Sen. Lindsey O. Graham (R-S.C.), the chairman of the Senate Judiciary Committee. Although he’s a staunch Trump ally, Graham has been criticized by some of the president’s supporters for not doing more to protect him.

Some Trump supporters, for example, advocate having Graham do his own investigation of Hunter Biden in front of the judiciary panel — including hauling in State Department officials who found Biden’s dealings inappropriate.

“I’ve seen a lot of conservatives starting to get kind of frustrated with Lindsey O. Graham because he goes on TV and says a lot of stuff but then . . . nothing ever goes anywhere,” said one Republican campaign operative close with Trump allies. “Republicans control half of Congress — and I think that they should act like it.”

In an interview Tuesday, Graham said he had not thought about the idea of calling either of the Bidens as witnesses in Senate trial, but he said he was ruling out his own committee as a venue.

“I don’t have jurisdiction over Hunter and Joe Biden, so we’re not going to call them at the Judiciary Committee,” Graham said, adding later: “That’s just not proper. I don’t have jurisdiction and I’m an institutional guy.”

When told his position might disappoint some conservatives, Graham pointed to other committees, including the Senate Foreign Relations Committee, suggesting they might be able to conduct such an investigation.

“Let’s look and see what’s out there,” he said. “The first decision I want to do is not turn the whole country upside down.”

Graham said last month he would invite Trump’s personal lawyer Rudolph W. Giuliani to appear before his panel to testify about “corruption and other improprieties involving Ukraine” — a prospect that Senate Democrats said they would welcome.

On Tuesday, however, Graham said he did not expect Giuliani to appear. Other Republicans said privately that calling Giuliani would be a bad idea given his involvement with a campaign to leverage foreign policy promises on political favors.

“I think they will claim privilege,” Graham said of Giuliani and the White House. “The question for them becomes, ‘Will that privilege stick?’ ”

Meanwhile, House Republicans have been using their time in the impeachment investigation to try to unearth new information that would cast the Bidens in an unfavorable light. Under GOP questioning during a recent closed-door deposition, Deputy Assistant Secretary of State George Kent testified that he had worried that Hunter Biden’s position with the firm Burisma Holdings would complicate efforts by U.S. diplomats to convey to Ukrainian officials the importance of avoiding conflicts of interest, The Washington Post reported. Kent said he took his concerns to the vice president’s office but was told Joe Biden didn’t have the “bandwidth” to deal with additional family issues because his other son, Beau, was battling cancer.

“Obviously based on testimony that I’ve heard, Hunter Biden’s role in Ukraine issues is certainly well-known, but also I think he could help the Senate understand if there were some legitimate concerns that needed to be addressed, whether they related directly to him or corruption more broadly,” said Rep. Mark Meadows (R-N.C.), a Trump ally who has been part of the impeachment depositions in the House. “I look at this more as a Ukrainian corruption issue than I do any particular individual.”

In a statement, Joe Biden campaign spokesman TJ Ducklo pointed to a newly released transcript of testimony from a former top Ukraine expert at State, Kurt Volker, who told lawmakers there was no truth to Trump’s allegations about Biden and Ukraine. Ducklo said, “It’s no surprise after today’s revelation . . . that some Republican senators might resist carrying the water of a president who is clearly spiraling and desperate to breathe new life into his pathetic lies.”

He added: “The sheer magnitude of Donald Trump’s misconduct becomes clearer each day, which is why Joe Biden believes Congress has no choice but to impeach him.”

If Republicans moved to call the Bidens during impeachment, Chief Justice John G. Roberts Jr. would likely have the final word. Roberts would oversee a Senate trial and has the power to accept evidence, dismiss the case and direct the proceedings — although he could defer those decisions to senators for a vote or be overruled by them.

Some Senate Democrats scoffed at the notion that Republicans would follow through with the Biden gambit, calling it a distraction from the substance of the evidence being compiled in the House.

“There was a stage where we were supposedly going to have Giuliani up here, so you can’t get too overheated by any of these proposals,” said Sen. Sheldon Whitehouse (D-R.I.). “They can’t defend what the president did, so they’re trying to change the subject.”

Some Republicans have been noncommittal about the prospect of going after the Bidens amid an impeachment trial. Sen. Susan Collins (R-Maine), a key possible swing vote in a potential trial, said Tuesday it would be “up to Lindsey Graham” on who should be called to his committee.

“I’m not going to get into that,” she said when asked about witnesses.

Sen. John Barrasso (R-Wyo.) said, “There has been a lot of attention to the Hunter Biden issue already,” adding he hasn’t “given much thought” to whether he or his father should be called as witnesses.

But others, like Paul and Kennedy, are ready to, as Trump told House Republicans recently, “take the gloves off.”

“It’s inevitable that when the trial comes to the Senate, one of the issues is going to be: ‘Did the president have a good faith reason to believe that Hunter Biden may have been involved in corruption?’ ” Kennedy said. “And if I’m correct in my analysis, then there will be a lot of time spent on what Mr. Biden did for the money.”

Seung Min Kim and Karoun Demirjian contributed to this report.