Most of the investigations focus on President Trump or his family business or a cadre of his advisers and associates, according to court records and interviews with people briefed on the investigations. They are being conducted by officials from Los Angeles to Brooklyn, with about half of them being run by the United States attorney’s office in Manhattan.

Unlike Mr. Mueller, whose mandate was largely focused on any links between the Trump campaign and the Russian government’s interference in the 2016 presidential election, the federal prosecutors in Manhattan take an expansive view of their jurisdiction. That authority has enabled them, along with F.B.I. agents, to scrutinize a broader orbit around the president, including his family business…

“The important thing to remember is that almost everything Donald Trump did was in the Southern District of New York,” said John S. Martin Jr., a retired federal judge who was the United States attorney in the Southern District during the Carter and Reagan administrations.