@OP, you should be good with at least a 1350W PSU, although I'd recommend going for the 1500W PSUs.
Originally Posted by khaosstrife
Just one issue with this, according the Enermax they only make the Platimax up to 1350W. The Enermax Maxrevo however goes up to 1500W. It's 80 Gold though.... not as good at Platinum.
Enermax does make a 1500W version of the Platimax.
Originally Posted by xxbassplayerxx
I was able to run four 7970 Lightnings at 1100/1600 along with a heavily overclocked i7 965 (for the HWBot Team Cup) on my AX1200. The power draw was probably close to 1300W because if I tried 1150 on the core the system would shut down almost immediately (all GPU's are good to at least 1250 in single card). I even had to use Molex to 6-pin and 6-pin to 8-pin adapters to get it all off the same PSU lol.
With this in mind, I'd say you'll be good with a 1500W PSU.
This is a bit off topic, but did you have to remove the GPU reactors with 4 Lightnings in Crossfire?