Just curious because I haven't seen it mentioned in the thread: what resolution are you trying to play it?
If I remember correctly most 6950s were 1GB and there may have been some 2GB models, but just for the record I have a GTX 760 4GB and when I max Just Cause 3 out at 1080p the game is using about 3-3.5GB of my v-RAM. I haven't got Fallout 4 but I imagine it's a similar story, so a 1GB or 2GB card doesn't cut it these days for maxing out the latest titles at 1080p I'm afraid. You want a new card with at least 3GB of RAM to even begin to think about maxing it. I would personally go for a 4GB card, maybe something along the lines of a GTX 960/R9 280X or a GTX 970/R9 390. I reckon if you got a newer card even if you keep your existing CPU and don't overclock it you will see a big performance benefit in games. Remember that the 6950 came out over 5 years ago now and it was a fairly mid-range card when it came out. It was a GTX 560 Ti rival!
And having two 6950s in CrossFire doesn't double the video memory.