As in his race against Mrs. Clinton, Mr. Sanders faces in former Vice President Joseph R. Biden Jr. a familiar face with a reservoir of good will among many black voters — a man who served two terms as the No. 2 to the first black president, and who begins far ahead in the South Carolina polls. Only now the race also includes two major black candidates, Senators Kamala Harris of California and Cory Booker of New Jersey, as well as another senator, Elizabeth Warren of Massachusetts, who is peeling off support on the ideological left.

Faiz Shakir, Mr. Sanders’s campaign manager, called the South Carolina challenge “significant but not insurmountable,” especially if Mr. Sanders performs well in the three preceding states, including Nevada.

“There is a really great possibility for South Carolina — I won’t say win — but I do think cutting margins significantly,” Mr. Shakir said, “particularly in the African-American community, which I think he will do much better with. That’s the path.”

After mostly minimizing South Carolina four years ago, if not seeming to downright disregard it at times, Mr. Sanders has returned with a previously unseen vigor. Once he had declared his candidacy in 2015, Mr. Sanders went more than three months before his first visit to South Carolina (one trip was postponed after the Charleston church shooting). This year, he has already visited seven times as a candidate; by this weekend, when Mr. Sanders visits on a college tour, he will have notched as many visits to the state as he made in the 2016 cycle.

“We’re going to give the vice president a run for his money,” said Nina Turner, a national co-chair of the Sanders campaign, who is black and who has been instrumental in the South Carolina strategy, visiting the state herself at least twice a month.

Mr. Sanders has unveiled two of his major policy proposals in South Carolina — his criminal justice plan and his “Thurgood Marshall Plan” for public education — as part of an effort to show his commitment to black voters in the state, advisers said. He has six offices here and 52 paid staff members (nearly three-quarters are people of color, according to the campaign).

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A Sanders spokesman in South Carolina, Michael Wukela, said the Vermont senator now counts 24 endorsements in the state — 20 of them from black supporters — compared with a total of only five at the end of the 2016 race. Members of the clergy are being wooed, as well.