It remains unclear whether the office of the Manhattan district attorney, Cyrus R. Vance Jr., will ultimately bring charges. The prosecutors have been fighting in court for more than a year to obtain Mr. Trump’s personal and corporate tax returns, which they have called central to their investigation. The issue now rests with the Supreme Court. 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.