Your PSU *will* run xfire'd 7850's, but only because the 7850's draw barely more than 100w at load.
The Apevia PSU is an alarmingly bad design. Frankly, I'm a little worried it might be causing your current system some long term damage.
It has four really weak +12v rails; the *strongest* rail only manages 180w. If your current video card draws more than that under load, and the card only has one 6 pin connector, I'd advise getting that PSU out of your system ASAP. That PSU is ok in your system if your card has two six pin connectors so you can use two rails to power it.
Although if you're running a 7850 already, you might be ok.
The strength of the 12v rail is more important in a gaming system than the total wattage of the PSU. Note the single 53a 12v rail in amuffin's suggestion. that'll give you 12v * 53a = 636 watts (that PSU actually has higher total output than it's rated 650w). Even split between two cards, each has over 300watts to work with, which is more than enough for almost any card in existence.
Also, make sure any new PSU you buy is at least 80 PLUS rated, if not 80 PLUS bronze/silver/etc. The Apevia is costing you more in electricity from less efficient conversion (and I just noticed it doesn't have active PFC, which is costing you even more).