Donald J. Trump has won just a single nominating contest, but his potential running mates already outnumber his presidential rivals on the campaign trail.

As he pursues a victory over Nikki Haley in New Hampshire that would send him on a glide path to the nomination, Mr. Trump seems to be holding casting calls for possible vice-presidential contenders onstage at his rallies and at other events.

His goals are clear: Show off the sheer breadth of his institutional support in the Republican Party. Inject a sense of inevitability into the race. And, of course, see which underling will butter him up the most.

On Friday alone, Senator Tim Scott of South Carolina, Senator J.D. Vance of Ohio and Representative Elise Stefanik of New York rallied supporters for him. Ms. Stefanik held a second event on Saturday.

The presence of all three, each of whom maintains a close relationship with Mr. Trump, generated headlines and fired up his base.

But joining Mr. Trump’s ticket can come with risks. Former Vice President Mike Pence twice ran with Mr. Trump, but his refusal to violate the Constitution to help overthrow the 2020 election led to Trump supporters storming the Capitol and threatening to hang him. Mr. Pence and his family were forced into hiding inside the Capitol to avoid the mob.

Mr. Scott’s stock seemed to rise with Mr. Trump after his endorsement of the former president on Friday, a move that showed the genial senator’s fealty and his surprising capacity for ruthlessness. In choosing Mr. Trump, Mr. Scott dealt a brutal rejection to Ms. Haley, his home-state compatriot and the woman who appointed him to the Senate.

Mr. Scott’s remarks at the Trump rally on Friday in Concord projected a stirring energy often lacking in own presidential bid, which he ended in November.

The crowd matched his excitement with shouts of “V.P.,” and Mr. Scott ended his fiery call-and-response speech by shouting with the audience, “We need Donald Trump.”

Mr. Trump noted Mr. Scott’s transformation.

“He was great, don’t you think?” Mr. Trump said after the rally to a Republican consultant, who insisted on anonymity to describe the private conversation.

Mr. Trump’s enthusiasm was a marked change from a year ago, when, after a lackluster debate performance by Mr. Scott, the former president raised eyebrows among some associates with offhand comments that the South Carolinian had not received much coverage.

Ms. Stefanik has also seemed like an increasingly decent bet to be Mr. Trump’s running mate, winning acclaim throughout the conservative world for her role in taking down two presidents of elite universities after a contentious hearing on antisemitism and campus protests.

At his Friday rally, Mr. Trump praised Ms. Stefanik, a one-time backbencher who rocketed to the party’s No. 4 House leadership job.

“Elise became very famous,” he said of her prodding of the college presidents, describing her questioning as surgical. “Wasn’t it beautiful?”

One potential hitch with a Stefanik pick: Mr. Trump mispronounced her last name as “STEH-fuh-nick” instead of “steh-FAH-nick.”

On Saturday, Trump supporters also greeted Ms. Stefanik with “V.P.” chants as she visited with volunteers at the former president’s campaign office in Manchester.

“I’d be honored — I’ve said that for a year — to serve in a future Trump administration in any capacity,” she told reporters.

At the Saddle Up Saloon in Kingston, N.H., Mr. Vance mingled with dozens of Trump supporters as reporters asked about his prospects to join the presidential ticket.

Mr. Vance, the best-selling author of “Hillbilly Elegy,” suggested he would be better utilized in the Senate during a second Trump term than as vice president. Still, Mr. Vance said, he would have to think about such an offer.

“I want to help him however I can,” he said.

Mr. Trump agonized over his pick for vice president in 2016, toggling potential picks until almost the moment of the announcement.

But during this campaign, Mr. Trump teased his vice-presidential pick before the first nominating contest last week in Iowa, where he said on Fox News that he had decided on a running mate but declined to offer a name. Still, a formal announcement could remain far off: Several people close to Mr. Trump have privately suggested that his comment was more showmanship than serious.

In Iowa, Mr. Trump also recruited a series of potential running mates to campaign for him: Representative Marjorie Taylor Greene of Georgia; Kari Lake, a Republican Senate candidate in Arizona; and Gov. Kristi Noem of South Dakota.

But the V.P. chants have grown much louder in New Hampshire.

At an event in Atkinson on Tuesday, Vivek Ramaswamy made an impassioned defense of Mr. Trump — less than a day after ending his own White House bid, most of which he spent glorifying the former president.

When the crowd chanted “V.P! V.P!” for Mr. Ramaswamy, an Ohio entrepreneur, Mr. Trump returned the approval.

Mr. Ramaswamy, the former president said, is “going to be working with us for a long time.”

Ms. Haley, who served in Mr. Trump’s administration as ambassador to the United Nations, has long been mentioned as a potential running mate.

But during Friday’s speech in Concord, Mr. Trump seemed to rule out that possibility.

“She is not presidential timber,” he said. “Now, when I say that, that probably means that she’s not going to be chosen as the vice president.”

Neil Vigdor contributed reporting from Kingston, N.H.

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