Every AMD GPU since TeraScale 3 (Radeon HD 5000-Series) has supported up to 3 Displays Per Card.
Now the caveat to this is., the Total (Native) Display Area must not excess the maximum Resolution that said GPU is capable of outputting.
For example if you're using a HD 6790, which supports up to 3840x3840... and you have 3x1920x1080
Well you're not going to be able to use them out of the box., because it'll be 5670x3240; this will exceed the 3840 in one of the axis that the Card can output.
And this will then just appear as if it doesn't support the 3 Displays as Windows / Mac OS will not allow it to be changeable in the Settings. Even though it'll detect it attached and "Working"... so how do you solve this?
Well simple, you have to use Eyefinity; this will allow you to setup and override the Defaults for a given Display.
In the example above 3x1920 (1080p) won't work... but 3x1280 (720p) will.
As I say., use Eyefinity (although this is now integrated into Radeon Settings, so the Display Tab in Adrenalin 2020 on-ward) and you want to override the Display Settings and Display Setup.
You'll eventually find one that works.