I got the steam version, can't rename the executable.
I was getting same problem with my 4870x2 card, with crossfire enabled and latest ATI drivers. I ran multiple test without any good result until I downloaded "Radeon Pro" at http://www.radeonpro.info
I made a new profile with my crisis 2 game, I've check in advanced Catalyst AI and set it to "normal". After it's done, go into Tweaks tab and force que CrossFireX Profile to Bioshock. Apply your settings by right clicking though your Crysis 2 profile. You can set some other tweaks by auto-disabling Aero and always forcing v-sync off, it help a lot on FPS aswell.
Launch the game by right clicking on your profile. Enjoy your CrossFire enabled and fully functionnal.

I was running at 44 average fps with miminum "high" setting and now i'm able to play on extreme settings at average 75fps.
Just to add to what he said, heres a few tips to get the best framerate possible, with zero flicker and no screen tearing. These settings worked perfect for me on my Radeon HD 6990 with Catalyst 11.3 CAP1 profile, and I thought I'd share. Follow Crytukz's instructions(minus disabling Vsync), in addition to what I'm adding, and I promise you will get a perfect Crysis 2 experience. I'm running on Extreme settings, at 1080p and 60FPS with NO performance dips the entire game. Stays at a constant 60, 61, 60, 61..etc.
1)Enable Vsync in game. This will ensure the framerate is matched to your monitor, preventing screen tearing.
2)Make sure the brightness setting is 50% or below, or you might get flicker.
3)In the "tweaks" tab of Radeon Pro, under "Direct3D Tweaks", check "Triple Buffering". This is the MOST IMPORTANT tweak you can use to ensure a smooth framerate with no screen tearing. This made a dramatic difference in FPS after I applied it, while eliminating input lag often caused by Vsync.
I've spent hours trying to get this game to work properly, and finally have come across a solution. Its unforutnate that this game takes so much work to run properly, but hopefully this will help all of you that are frustrated by this mess. I'm not certain that this will work for everyone with crossfired AMD cards, but I can assure you guys it will work with the 6990. Hope this helps and good luck.
Tried it with my 4870 CFX and it didn't do anything about the flicker. With one 4870 I can get 60fps at 720p with Extreme Graphics and no AA, AF, Motion Blur or SSAO. It's a pretty good balance all things considered but with Crossfire I can get 45-50+FPS at those same settings at 1080p but have to deal with the god damn flicker.
Trying 1080p with those settings on one 4870 is 28fps. Sadface.