I'm not sure the first option is possible. Could I purchase a 2nd Nvidia card and would it run the 3 monitors well?
If your intention is to play games at 3 monitor, Yes, you need to purchase another GTX 550Ti to support 3 monitors. This is nVidia way for series 5XX cards. But even 2x550 Ti will not play smoothly on triple monitor. You need more powerful cards with large VRAMS (2GB preferably more ).
Triple monitor can be supported by single nVidia 6XX cards but it should be at least 670 to run smoothly.
AMD options should be at least 2x6950 or single 7950 but you will also need special adaptors or display ports in your monitors.
How much is your budget for both the video cards upgrade & the 3 monitors?