FWIW, Thomas Mitchell had significant roles in three best picture nominees in a single year (1939): Gone with the Wind (as Scarlett’s father), Mr. Smith Goes to Washington (as a cynical reporter) and Stagecoach (as the alcoholic doc, for which he won the Oscar for supporting actor)
So did John C. Reilly in 2002. He was Julianne Moore’s husband in The Hours, the corrupt police officer in Gangs of New York, and Amos Hart in Chicago, for which he was nominated for Best Supporting Actor. It was a particularly impressive hat trick for him because there were only five Best Picture nominees, as opposed to ten in Mitchell’s year.
It seems that being of Italian descent and working with Martin Scorsese ups the odds for you of being a a best picture nominated film.
I’m inclined to think the answer is Jack Nicholson, but one star who’s been in 9 Best Picture nominees is William Holden:
William Holden was in:
Our Town
Sunset Boulevard
Born Yesterday
The Country Girl
Love Is a Many Splendored Thing
Picnic
The Bridge on the River Kwai
The Towering Inferno
Network
Maybe there’s a Holden flick I’ve missed, but he’s got 9 for sure.