Tuesday’s primaries in Pennsylvania, Connecticut, Maryland, Delaware and Rhode Island could bring Donald Trump close to securing the delegates he needs to win the Republican presidential nomination, though probably not all the way there. After a series of missteps, he seems to realize that he needs to improve the style and substance of his campaign among both Republicans who resist him and the electorate at large.

That’s why Mr. Trump has hired a Henry Higgins to work on his comportment. Paul Manafort, Mr. Trump’s new campaign chief and an old-guard Republican strategist, has eclipsed the abrasive Corey Lewandowski and his nonnegotiable “Let Trump Be Trump” approach. Mr. Manafort’s ambition is to turn this Eliza Doolittle into a candidate more acceptable to decent society, in time for the general election.

Mr. Manafort rolled out his Pygmalion project with a PowerPoint presentation behind closed doors at the Republican National Committee retreat in Florida last week. “The part he’s been playing is evolving,” Mr. Manafort assured the Republicans. Mr. Trump doesn’t really mean it when he says things like he’ll deport 11 million immigrants, or block Muslims from entering the country, or kill terrorists’ children, or when he maligns women. He’s doing all that, Mr. Manafort suggested, to win the primaries; come the general election, Mr. Trump will bloom into his truer (and presumably kinder and gentler) self.

Mr. Trump himself has been saying the same thing in private for months, including in regular calls to members of Congress and Republican leaders.