Well I'm not sure what to think then. Almost always if you can get two to work in any combination, but not a third, it is because there are more than two legacy connections.
However, active adapters solve the problem of legacy connections, so if legacy connections were the problem, it should have been fine with you using active adapters. You are 100% certain they are
ACTIVE adapters? And not Apple-brand active adapters, because those are known to have problems with third party monitors.
No, VGA DVI and HDMI are all legacy connections, so HDMI capable does not help. DisplayPort and Thunderbolt are not legacy.
If you want to know more about how/why this happens on AMD cards beyond two monitors,
see my post here that explains it in detail.
It would help me to help you if you could list all the ports you have on the card and all the ports you have on each of the three monitors, and what adapters you are using.