As the Democrats focus on a nominee for 2020, Republicans are already privately, quietly speculating about 2024. Here is a scorecard. If PresidentTrump wins re-election, at least three persons in his administration’s inner circle would have plausible claims to extend his legacy for another four or eight years.

The vice president: Vice President Pence has been traveling the country assiduously cultivating state and local elected politicians and party officials. He has executive experience as a former governor of Indiana and congressional experience as a former member of the House. He lacks Mr. Trump’s outsized personality, but after eight years, that may come as a relief to some.

As vice president, Mr. Pence is associated with the president’s record, for better or worse. He’d be 65 on Inauguration Day, 2025. The vice-presidential succession is a common model; Vice President George H.W. Bush rode President Reagan’s success to victory, and Vice President Gore almost did the same after Bill Clinton’s presidency. With Trump, one can’t count on the conventional approach.

Family: The president’s son-in-law, Jared Kushner, would be the first Jewish president, unless Senator Sanders, Mayor Bloomberg, or Senator Bennet defeats Mr. Trump in 2020. Mr. Kushner’s signature policy achievement, bipartisan criminal justice reform that freed nonviolent drug offenders, was the subject of the Mr. Trump campaign’s moving Super Bowl commercial: “Thousands of families are being reunited.” Mr. Kushner has also taken the lead on Middle East peace; if he can get a deal on that, he would have a second substantive accomplishment on which to run.

Ivanka Trump: Don’t expect Jared and Ivanka to both seek the Republican nomination. The last name “Trump,” though, has the potential to be as powerful with the Republican base as “Bush” used to be, or as “Kennedy” used to be with Democrats. She has fewer policy wins to point to than Mr. Kushner does but has greater stage presence. If her father were to campaign for her, it could be plausible. It’d certainly be ironic if the legacy of a president criticized for his supposed misogyny turned out to be his daughter becoming the first woman president. Donald Trump Jr. also gets mentioned but seems to me a longer shot, as, unlike Mr. Kushner or Ms. Trump, he has no official White House role.

The Fox News crew: Trump was launched from television (“The Apprentice”) to political stardom. Sean Hannity and Tucker Carlson both have large, loyal, nightly conservative audiences of millions and are generally aligned ideologically with Mr. Trump. Like Mr. Trump did, they’d start with significantly higher name recognition than most Republican governors or senators.

The diplomats: The former governor of South Carolina, Nikki Haley, is popular on the speaking circuit and did a fine job in her stint as Mr. Trump’s ambassador at the United Nations. She can tout her experience at the world body while also maintaining a slight distance from an administration in which she no longer serves.

Secretary of State Pompeo, like Mr. Pence, has congressional experience, having served as a member of the House of Representatives from Kansas. Mr. Pompeo, a former director of the Central Intelligence Agency, is a graduate of West Point and Harvard Law. His recent clash with NPR’s Mary Louise Kelly could hurt him with the rest of the press but help him with the Republican primary electorate.

The non-Trumps: If Mr. Trump loses in November, it widens the field to candidates less closely associated with him. The governors of Texas and Florida, Greg Abbott and Ron DeSantis respectively, start with the advantages of being from states with lots of Republican delegates and donors. Senators are often presidential candidates-in-waiting; current Senate Republicans include, among others, Tom Cotton of Arkansas, Josh Hawley of Missouri, and Ben Sasse of Nebraska.

One of the criticisms of Trump is that he has weakened the Republican Party by turning it into a one-person personality cult. It is true that Mr. Trump has a way of making other politicians seem small by comparison. If he is elected, though, it’ll be in his interest to build up at least some of the people on this list.

Presidents eventually come to the realization that the only way to cement the legacy and avoid spending a second term entirely as a lame duck is to have a successor that extends the eight-year run to 12 or even 16 years. It’s a rare feat in American presidential politics, but then, so are many of Trump’s other accomplishments.

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Correction: 2024 is the year to which the headline over this dispatch refers; the year was given incorrectly in an earlier edition owing to faulty editing.