– President-elect Donald Trump is broadening the field of candidates for secretary of state as his transition team remains divided nearly a month after the election over how to fill the most prominent gap in his prospective Cabinet.

Top adviser Kellyanne Conway told reporters Sunday that the search had expanded beyond the four men thought to be under consideration and that Trump planned to interview additional candidates early this week.

Those new candidates appeared to include John R. Bolton, an ambassador to the United Nations under President George W. Bush; Jon Huntsman Jr., former Utah governor and ambassador to China under President Obama; Rex W. Tillerson, president and chief executive of Exxon Mobil; and Sen. Joe Manchin, D-W.Va.

Asked about the search on ABC, Vice President-elect Mike Pence mentioned Bolton as a potential candidate and said others could be added to the list. Bolton met with Trump for about an hour on Friday and Tillerson is set to meet with him on Tuesday, according to two people briefed on the meetings.

Despite their differences over the Iraq war, which Bolton ardently supported, Trump said during the campaign that he turned to Bolton for military advice and called him “a tough cookie.”

The transition team had previously signaled that the group under consideration had narrowed to four men: Mitt Romney, the 2012 Republican presidential nominee; Rudy Giuliani, former mayor of New York and a close ally of Trump; Sen. Bob Corker of Tennessee, chairman of the Foreign Relations Committee; and David Petraeus, retired general and director of the CIA under Obama.

An announcement of a selection for the post is not expected for at least several more days.

In an audition of sorts, Petraeus appeared on ABC to highlight his foreign policy experience in the military and his work abroad in the private sector. He also sought to put behind him a potentially significant hurdle to his candidacy: his mishandling of classified material while he was a top general. He pleaded guilty to a misdemeanor charge in 2015 and was forced to resign as CIA director.

“Five years ago, I made a serious mistake,” Petraeus said. “I acknowledged it. I apologized for it. I paid a very heavy price for it, and I’ve learned from it.” But he added that it was up to others to “determine whether that is indeed disqualifying or not.”

The wrangling over who should be America’s top diplomat comes as Trump’s team continues to face questions about his protocol-shattering phone conversation with the president of Taiwan last week, which angered China and rattled other Asian nations. Bolton advocates closer ties with Taiwan as a means of putting pressure on China, arguing that Beijing’s growing power in the region should be checked.

Trump’s advisers are battling, at times publicly, over whether he should choose from among his campaign loyalists or go outside that circle, a move that could alienate base voters who were angry at the GOP establishment. Much of that wrangling has centered on Romney, who was among Trump’s fiercest critics during the campaign.

Trump has told aides that he believes Romney would “look the part” as the face of U.S. outreach to the world and would make a fine secretary of state.

But Conway, who has been openly critical of Romney, continued to attack him during a “Fox News Sunday” appearance, saying that the backlash to his candidacy among Trump’s core supporters had been “breathtaking.”

Asked if her criticism of him was appropriate, she said, “I would turn the question around and ask, was it appropriate for Governor Romney to stick his neck out so far in attacking Donald Trump, and never walking it back, never encouraging people to support the nominee once Mr. Trump had won the nomination squarely and fairly.”