A widely watched lawsuit between a billionaire and top art tycoon has expanded to include one of the most private and powerful families in the art world.

Last week, a judge granted a motion by billionaire financier Ronald O. Perelman to depose members of the Mugrabi family as part of a lawsuit between Perelman and art megadealer Larry Gagosian. According to people familiar with the case, the depositions are scheduled for September and could delve into the financial relationships and dealings between the Mugrabis and Gagosian.