That computer seems more than sufficient.
With the graphics settings turned down, you should have no problem with that. If anything, that GPU is overkill unless you are trying to run multiple 4k monitors.
But first, did you try running some multibox software to manage the resources? Both ISBoxer and Eve-O Preview have the ability to minimize the CPU and GPU use of background clients. Unless you need them all open and fully responsive at all times, it goes a long way to stretching your system’s resources among multiple clients.
In fact, you might want to experiment with that on your current system first. I would suggest trying Eve-O Preview (it’s free!) and setting up the ‘Minimize inactive EVE clients’ feature to see how that works. Basically only the client in the foreground gets full resources and the CPU/GPU use of the background clients is throttled.