But lately, Mr. Vance’s office has stepped up its efforts, issuing new subpoenas and questioning witnesses, including some before a grand jury, according to the people with knowledge of the matter, who requested anonymity because of the sensitive nature of the investigation.

The grand jury appears to be serving an investigative function, allowing prosecutors to authenticate documents and pursue other leads, rather than considering any charges…

Over the years, employees and executives inside the bank thought that Mr. Trump was overvaluing some of his assets by as much as 70 percent, according to current and former bank officials. Deutsche Bank still decided to lend Mr. Trump’s company hundreds of millions of dollars over the past decade, concluding that he was a safe lending risk in part because he had more than enough money and other assets to personally guarantee the debt.