The multibillion-dollar family office for one of America’s wealthiest families is going through a shake-up.

New York-based Ziff Brothers Investments plans to gradually shutter its US hedge fund and give some of the fund's top people money to start their own independent firms. Some of the fund's money could be shifted to Ziff's other internal hedge fund, based in London, or to external hedge-fund managers, people familiar with the firm said.