I don't know if JFK's father Joe Kennedy (a bootlegger) was 'celebrity' material, but he had plenty of Mob connections.

James Caan was a New Yorker and wanted to be a mobster, but I very much doubt he is of Italian descent. I never really knew what to make of Caan to be honest.

Elvis Presley took out a hit on karate instructor Mike Stone when Stone hooked up with Priscilla Presley after her split from Elvis.

Presley had an entourage of minders and bodyguards (and freeloaders) called 'The Memphis Mafia', but their rough treatment of fans was causing law suits. Red West was one of the key Memphis Mafia members and he was the one who made plans for the Mike Stone hit until Elvis backed away from the idea.

Interestingly, in 1976 James Caan married Sheila Ryan, an ex-girlfriend of Elvis, but the marriage only lasted a year.