You can install the most expensive card available. You will have increasingly faster performance with each new card. But your card's performance would have greater and greater diminishing returns past a certain point.
I finished a budget build for someone awhile back with an Athlon II X4 640 and an O/C'd EVGA GTX 650ti SSC. It was an amazing gamer at 1920x1080. Really surprised me. BF3 (Campaign) at Ultra. Crysis 2 w/DX11 and the Hi-Rez tex pak at highest settings. Crysis 3 on High using SAAO. All playable with smooth frame rates. I then tried an MSI Twin Frozr GTX 560 OC I had laying around and it seemed to perform slightly below the 650ti SSC. So I would estimate the GTX 650ti Boost or possibly a GTX 660 would be about the max before bottle neck got serious.
As far as putting an actual number on FPS, that is hard to do. It would depend on the game, the resolution you would game at, and several other factors. Some games are GPU intensive and some are CPU intensive.