The GTX 770 supports up to 4 displays, so there's no issue with the 3rd TV. The issue is with the 4K resolution. The 770 only has HDMI 1.4, which is only enough for 4K @ 30hz. That might be okay for movies/TV I suppose, but is going to be pretty terrible for gaming. Having said that, the GTX 770 is going to seriously struggle to run games at 4K anyway.
Does your TV have a displayport input? Because that would give you 4K @ 60hz. Otherwise, can you live with just 30hz on your display? I'm not sure I could, but you might be prepared to.
Nvidia was playing around with lowering the colour space to get 4K@60 over HDMI, but I'm not sure whether it requires TV/display support. It might be an option to investigate that though.