That depends is the answer based on the info you gave. nVidia cards will not work in conjunction with ATI/AMD cards, so no mixing of GeForce and Radeon HD. nVidia uses the terminology SLI, AMD went with CrossFire, but they refer to the same basic idea.
nVidia cards are kind of notoriously picky about which will work in SLI mode, generally your safest bet is to have two identically matched cards. AMD cards will often play nicely with newer/older siblings, but it's not a case of just pick any two CrossFire enabled cards. On a hardware review site or two you should be able to find a matrix that breaks down what AMD cards will work together in CrossFire mode, and something similar for nVidia and SLI.
Since you already have an ATI/AMD card, you'd need another ATI/AMD card for this to work. This is assuming you have a motherboard with at least 2 x16 PCIe slots for both video cards (or don't mind one card being crippled by an x8 or even x1 slot -- which if you were using the second card purely for things like PhysX support, might not be a disadvantage) and have a PSU that not only has sufficient capacity, but the proper number of adapters for two or more video card configs. For the most part, all but the most hardcore gamers with a lot of time and money to burn, find that it's simply not worth it. Based on the reasonable assumptions that can be made about your overall technical expertise based on this one post, you need to spend quite a bit more time on some of the fundamentals before you're ready to tackle a SLI/CrossFire project.