The value of an autograph, auctioneers will tell you, depends largely on four factors: scarcity, demand, authenticity and what it’s signed on. When it comes to presidents, the living ones’ signatures tend to go for less than the dead ones, said Lori Ferber, who runs a presidential memorabilia site.

But occasionally the factors align to propel a living, prolific signer into the four- to five-figure zone. Since President Trump took office, the signed objects that have landed there include a book inscribed with: “Dear Carol I will never change the hair” ($3,000); a recalled Newsweek pronouncing Hillary Clinton “Madam President” ($5,435); and Mr. Trump’s sketch of the New York City skyline ($29,184).

Now, in the wake of his acquittal by the Senate, one item appears poised to surpass the others: a printout of the House Judiciary Committee’s impeachment report that an auction site says was signed by the president at a rally in Michigan on Dec. 18, just hours before the House voted to impeach him. With more than two weeks of bidding left, the price had already reached $17,000 by Wednesday night.

Les Gold, founder of American Jewelry and Loan and star of the TV show “Hardcore Pawn,” told The Detroit News recently that he expected the document to sell for “$100,000 to $500,000.”