But neither can he fade, those close to him say, if he wants to live without regret — a through-line in dozens of conversations with friends, relatives and former advisers. They cite no shortage of motivations for his candidacy: his Mormon faith and its emphasis on service; the memory of his father; his irrepressible ambition, coaxed by a family-wide conviction that he is a singular leader of his times, if only the voters could see it.

“Everyone is running out of a burning building. Mitt’s running in,” Mrs. Romney said in an interview. “This is Mitt, runs into burning buildings.”…

Mr. Romney plans to avoid a similar coda. He has already spoken in private about serving two terms. He hopes to join the Senate Foreign Relations Committee, among other assignments. And he has told supporters he wants to become a leading voice on fiscal discipline and immigration policy — about which he has said he is “more of a hawk” than the president.

“He’s hesitant to even bring up his name,” Josh Romney said. “He doesn’t want it to be about Donald Trump.”