Yeah, you need to be in at least three juggernauts to be in contention, and a bunch of one offs. I was thinking maybe Malden who had four movies with three or more Oscars (On the Waterfront 8, Patton 7, Streetcar! 4, How the West Was One 3) but no singles so he topped at 22. Brando had a couple solid performers, but Waterfront was his only huge one, leaving him at 23. O'Toole had 19 for his three BP winners (Last.Emperor 9, Larry of the Sands 7, Lion in Winter 3) but only two one offs, so 21.
Of course, we are talking about credited roles, or someone like Franklyn Farnum (non-exhaustive count: 52) or Bess Flowers (not even going to try) clearly wins. But the imdb entry "Sarah Siddon Award Guest (uncredited)" should not count. Though admittedly that knocks Ward Bond down.