Hmm, I am not sure a second graphics card will give you the wanted boost. It is probably your CPU being the bottleneck. One tip for battlefield though, limit it to 100fps or even less, to save cpu power.
I am currently using an i7-4770 with a 7850 and could stream 720p 30/60fps on the very fast preset without loosing too many frames in BF4. Although I personally still prefer to either use quicksync or my second PC to do the recording/streaming and keep the fps on a totally steady 100 in every situation.