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.