You need a video card the is either capable of outputting video to three monitors from one card, or you need an additional graphics processing unit. Your card does not appear to have this capability.
Many systems have integrated graphics which usually will allow to run the integrated graphics along with a card. With your card, this would allow you 3 three monitors; 2 on the GPU card, one on the integrated GPU. You might need to dive into your BIOS to make it work though and in some BIOS's they don't allow both the integrated graphics and a dedicated GPU to be run at the same time. It all depends on your system.
If you do not have a integrated graphics that allow a third monitor, then you need to buy a second card. Depending on your requirements, depends on the card you should buy. If you need maximum compatibility AND performance, then you should buy a card that is covered by a single driver install. That is, the driver from AMD's website will cover more than just your card. So for you should find a card that uses the same driver install.
In reality though, just about any second ATI SHOULD work; but sometimes there are compatibility issues no matter what you plan on. So If you are ok with a small chance for possible troubleshooting, or lower performance (usually only an issue with games or design programs), then you can buy just about any other ATI card and try it out. You do not need a high performance card if you are going to be using it for watching movies, browsing the internet, and office apps. And sometimes, if you put a game or design app on the monitor with the more powerful card, it shouldn't affect gaming performance either; but this is not always the case. Again, it all depends on your system, the cards, and their drivers and software.
Many times, NVIDIA and ATI cards will not play so nice with each other so I would stick with the same GPU chipset maker for two cards to increase your chances of it working without a hitch.
Another option is to find a product that will simply add a third monitor via something like USB. There are many odd products out there, but not many of them will work reliably.
Final option is to buy a card that is designed to output to three or more monitors.