If this is still an active thread, I contacted Saphire about their HD7770, and they said it can handle 3 monitors, in extended desktop mode; not spanned or Eyefinity. AMD support replied that theirs handles only 2. Another thing to note is the max res. My question to both OEMs was actually how many 1920x1200 monitors in extended desktop mode could I run, simultaneously. Saphire said the max res output was 5670X1200, which is just shy of 3x1920x1200, but it would work for my 3 monitors. I'm currently using a HIS HD5770 for 3x1920x1200, and I get occasional display issues. In theory, on a PCIE3 MoBo, you could put 3 HD7770s and power up to 9, but I expect you'd experience some display issues, and I'm certain you'd log GPU/CPU resource errors.
*on a side note, if anyone knows of a card that's better suited to 3+ extended desktop displays (at 1920x1200), for less that $1000, please let me know.