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Not sure if this is also true in macOS.


From AMD support page:

Connectivity Requirements: AMD Eyefinity technology is supported by graphics cards in the ATI Radeon™ HD 5400 series and higher. These cards can support up to six monitors (depending on the model), subject to the following restrictions:

• A maximum of 2 legacy monitors (VGA, DVI or HDMI) can be enabled simultaneously, provided that each monitor is connected either directly or via a “passive” DisplayPort™ adapter/dongle. “Passive” adapters/dongles will NOT support more than 2 legacy monitors.

• To enable support for more than 2 monitors, “active” DisplayPort™ adapters/dongles are required (or monitors with direct DisplayPort™ connectivity must be used).

• Approved “active” adapters have no general connectivity restrictions with AMD Eyefinity technology.


But AFAIK, some cMP users can drive three monitors via a single HD5770 with proper adaptor(s).
 
I have 3 displays running off one XFX 5770 (EFI boot flashed).
All three are technically “legacy” displays.
1x HDMI
1x DVI
1x DP to DVI *active* adapter

If it isn’t a real display port monitor it must be an active adapter.
[doublepost=1533739094][/doublepost]Also I have a second card in the machine being a 5450 running 2 displays on that. (5 total)
I know of no technical limit to the number of displays OS X will support. So depending on the exact model of 5770 you have you will likely be able to do 6 displays from the two cards.
 
You should be good with the Apple 5770s. I've heard that other PC based cards may only allow 2 monitors per card as the ports are mapped differently.
 
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