new dog to move in?

I believe that canines (not humans) are the best judge of compatibility with other canines. In this case, where the border collie has been around the other three dogs and acts afraid of them, I think your concern for safety is warranted.

I would be very careful. Not because they are pit bulls, but because they're a pack. From my own experience, a pack of dogs won't accept a new dog into their home. Obviously, if they are extremely well behaved, obedience trained, K9 good citizen certified, then that changes a situation. They all can do well with the new dog when the owners are around. But they should never be left alone. The new dog must be kept separated. Good luck.