While he has not been charged with a crime, many of his associates have faced either criminal charges or stiff regulatory penalties. That includes partners in the taxi business, doctors for whom he helped establish medical clinics and lawyers with whom he worked…

In addition to his legal and taxi businesses, Mr. Cohen has had a seemingly charmed touch as a real estate investor. On one day in 2014, he sold four buildings in Manhattan for $32 million, entirely in cash. That was nearly three times what he paid for them no more than three years earlier.

“This is the type of person you’d see most bankers steer clear of,” said Ben Berzin, a retired executive vice president and senior credit officer at PNC Bank who clashed with Mr. Trump in the early 1990s over loans to the future president’s troubled Atlantic City casinos. The speed with which Mr. Cohen successfully flipped real estate stands out, Mr. Berzin said. “You have to ask what’s going on.”