Expelling Mr. Moore could present an advantage to Senate Republicans since it could create a vacancy and set off another special election in Alabama, giving the party a chance to find a new candidate. The uproar over his candidacy is also providing Mr. McConnell and his allies with evidence that the effort to oust establishment Senate Republicans being led by Stephen K. Bannon, the former adviser to President Trump, could be disastrous if Mr. Moore is an example of who they intend to support.

But the fight over Mr. Moore could also elicit a harsh backlash from conservative activists aligned with Mr. Bannon and deepen the party split that is already looming as an obstacle in the 2018 midterm elections.

Republicans are also weighing the potential of a write-in campaign behind an alternative candidate. It worked for Senator Lisa Murkowski in Alaska in 2010, but such successes are exceedingly rare. A write-in campaign by a Republican could split the party vote and bolster the chances of the Democratic candidate, Doug Jones, a former federal prosecutor. Mr. Jones could also win outright, a result that could solve many thorny problems for Mr. McConnell but would leave Republicans with one fewer seat and a narrow 51-49 majority when they are already struggling.

Mr. McConnell does not appreciate such complications. When Mr. Craig was arrested and pleaded guilty to disorderly conduct in the airport sting, Mr. McConnell set out to prevent him from even returning to the Capitol to avoid a spectacle. The leadership stripped Mr. Craig of his committee leadership positions and made clear that if he decided to return, he would face additional ethics scrutiny.

Mr. Craig quickly announced he would resign his Senate seat. He then reneged and decided to serve out his term, but the ethics committee admonished him for his behavior and he was treated as an outcast by many of his colleagues.

In the Packwood case, Mr. McConnell delivered findings on the Senate floor, describing his colleague’s “physical coercion” of women and “a habitual pattern of aggressive, blatantly sexual advances, mostly directed at members of his own staff or others whose livelihoods were connected in some way to his power and authority as a senator.” Republicans ultimately lost that seat after Mr. Packwood’s resignation.