I was just thinking about the Williams team and its history. Since they entered F1, they've run Cosworth engines during 3 separate stints (badged as Ford in the 70s/early 80s), Honda engines, Judd engines, Renault during 2 stints (including a couple of years with re-badged Renaults, which I wouldn't consider a "different" engine maker necessarily), BMW engines, Toyota engines, and now Mercedes engines.
That's 7 engine manufacturers, 10 if you consider Ford separate from Cosworth and Mechachrome/Supertec distinct from Renault.
Has any single team or even chassis manufacturer run with more engine suppliers during its F1 existence? I'd guess Lotus would be close, especially if you consider the current team a continuation of the original (a stretch, to be sure), and maybe Cooper in its various guises?