I’ll be very surprised if anyone can answer this question. There is a good chance that no ‘family’ actually ownes a fleet of aircraft (give or take the guys east of Israel). More likely you will find them registered to a company. That company will have shareholders which may consist entirely of one family. But who cares?

Look up Gold Air if you are really interested. If that doesn’t fascinate you, then you may note that they have a connection with Ann Summers. Now you’re interested!