In a crowded, 21-candidate primary for one of Missouri’s U.S. Senate seats, Republicans and independent power players are clamoring to defeat President Trump’s apparent favorite, Governor Greitens, who most see as a compromised candidate.

Earlier this month, Mr. Trump expressed a clear preference for Mr. Greitens while brushing aside one of the former governor’s top competitors, Representative Vicky Hartzler. “Eric is tough, and he’s smart,” he said to One America News. “A little controversial, but I’ve endorsed controversial people before. So we’ll see what happens.”

Of Ms. Hartzler, Mr Trump wrote: “I was anything but positive in that I don’t think she has what it takes,” after dismissing Ms. Hartzler’s calls “asking for my endorsement.”

A professor of political science at the University of Missouri, Peverill Squire, argues that Mr. Trump is telegraphing his support for Mr. Greitens even though he hasn’t officially endorsed him. “There are a number of people on the Republican side who would like to think of themselves as Trump’s favorite,” he tells the Sun. “At the moment it seems like Greitens is his favorite.”

He notes that though the Missouri attorney general, Eric Schmitt, one of the three frontrunners, has seen some support from Mr. Trump in the past, he is “tangential” to Mr. Trump and “not someone that Trump knows well.”

Mr. Greitens resigned in 2018 after allegations of a sexual relationship with his one-time hairdresser, of whom he had allegedly taken explicit photographs without her permission.

Following the former governor’s 2020 divorce proceedings, a child custody battle has unearthed more accusations, including child abuse and “unstable and coercive” behavior, according to Sheena Greitens’s March affidavit.

She said that behavior included “cuffing our then three-year-old son across the face at the dinner table in front of me and yanking him around by his hair.” Ms. Greitens claims she has photos and documents to back up her allegations.

Republicans in Missouri and elsewhere have looked at Mr. Greitens’s prospects of winning the primary, and decided to take action.

Rex Sinquefeld, a Republican donor who has contributed more than $41 million to GOP campaigns in Missouri over the past decade, has allied with Nebraska’s governor, John Peter Ricketts, and the CEO of Anheuser-Busch, August Busch III, to defeat Mr. Greitens.

Mr. Ricketts, who was once a political ally of Mr. Greitens, said at a London press conference that the governor was “unfit” to be a senator and “not fit to be in office.”

Beyond the Republican Party, independents are coalescing around a candidate to challenge Mr. Greitens, a former Republican and U.S. attorney, John Wood.

Mr. Wood has the backing of a Missouri institution, Senator Danforth, who contributed $5 million to a PAC supporting Mr. Wood’s campaign and plans to raise an additional $20 million to $40 million before November.

“We’re not in this to be a spoiler,” Mr. Danforth told the Missouri Independent. “That’s for sure. We’re in it to win it,  and I believe that we can win it.”

Mr. Squire argues that if Mr. Greitens succeeds in winning the August 2 primary, it would create a “worst case scenario” for the GOP. 

“You’d give St. Louis suburban Republicans, particularly women, the chance to decide who wins in the general election,” he said. “Everything that has come out about Greitens in his divorce proceedings is not something that most suburban voters will feel comfortable supporting.”

When combined with a third party candidate backed by an old-school conservative politician, a weak Republican candidate could land the GOP in a tight race.

The latest polling from SurveyUSA shows that in the general election, Mr. Greitens would have a six-point lead over either the Democratic frontrunner in the general election, attorney Lucas Kunce, or Trudy Busch Valentine.

Polling from the Trafalgar Group had previously shown Mr. Greitens in a dead heat with a Democratic state senator, Scott Sifton, who has since withdrawn from the race.

A political scientist at Washington University in St. Louis, Daniel Butler, argues that the key for Republicans will be ensuring someone other than Mr. Greitens is at the top of the ticket — something he thinks is increasingly less likely.

Mr. Butler suggests that Mr. Greitens’s relatively “extreme positions” may be enough to garner the largest plurality in the primary. He argues that Mr. Greitens “appeals to 30 percent, which may be all you need” to win the primary.

He says increasingly polarized primaries turn off moderates from voting and that this phenomenon could help Mr. Greitens clinch the nomination. An endorsement by Mr. Trump, he argues, could also be just enough to push him over the edge.

A senior data scientist at Decision Desk HQ, Liberty Vittert, argues that the situation is a little more nuanced but that Republicans should be concerned about Mr. Greitens’s possible victory.

“Whoever is the Republican candidate has a huge advantage but it is qualitatively true that a different candidate from Greitens would fare better in the general election,” she tells the Sun.

“If he gets the Trump endorsement he has a good chance of winning the primary,” she added. “If I were Republicans I would be worried if Greitens wins.”

Mr. Greitens’s campaign did not respond to a request for comment.