The video card manufacturer may not include support. I have 2 HIS 7750 cards which do not Crossfire. HIS has 4 models of the 7750 based cards, if you compare features it shows that only 1 of the 3 support the Crossfire standard.
I looked at AMD's chart before buying the 2nd card, because I didn't see Crossfire support listed by Newegg & thought it was an oversight. After many attempts to get the 2 matching cards to work, I found out HIS left that feature out on the model I bought.
This is an old thread that has been answered. But to follow up...
I installed a 2nd HD 7750 OC card and it worked fine in CF. But as Onus rightly surmised, the performance was lacking. Faster than a single card for sure, but not enough to warrant the cost of the 2nd card.