The PC 6870 support in OSX is a bit sketchy. Don't think anyone has got 4 monitors running.
I believe I have read threads on here of people running 3. You mention the 'PC' is there a 'Mac' version of this card?
Nope. Only PC "officially" for 6870. Mac users have got them to work fairly consistently but as Cindori points out, maybe not for 4 display's in OS X.
If your main goal is the 4 displays I'd just get a 2nd 5770. Easy and if needed you could Crossfire them in Windows for gaming but I know that was not a priority for you. But 2 display's on each 5770 would work just great.
I should amend my first post, four displays would be nice, three would be fine too. But if there is zero improvement in performance, then its not really worth it. I have three displays working now, but my third is a bit of a kludgy setup using a Matrox USB display adapter, it works but the monitor plugged into this is a bit sluggish when I change virtual desktops.
I do game a bit in windows via bootcamp. I do use photoshop, Adobe Lightroom, thats about it graphics wise. The 6870 is cheap enough and I could likely offset the cost by selling my 5770 if thats what I decide to do. I may just pick one up this weekend and try it out. The few things that don't work in OSX due to the fact its a PC card, don't really bother me.
I run a 6870 and can get only two monitors running off of it. I would love to know how to get three going. I currently use a gt120 to drive two additional monitors