Here is the results by my calculation:

16 Martin Sheen in Apocalypse Now
14 The Butler in Dinner for One
13 Walter Matthau in Earthquake
12 Nicholas Cage in Leaving Las Vegas
11 Lee Marvin in Paint Your Wagons
10 Cary Grant in North by North West
9 Robert Mitchum in El Dorado
7 Olly Reed in Oliver
6 Lee Marvin in Shout at the Devil
6 Lee Marvin in Cat Ballou

Lee Marvin drew with himself there.