quote; One from a three wire coming in from the middle.
WE, or at least I, have no idea what that means, but it could indicate several different issues all of which are completely different and would require specific wiring to extend them. The key item is that since you do NOT know where the "fourth wire" goes, you may not have the proper experience to do what you want to. The results of improper wiring range from a tripping circuit breaker, to injury or death, all the way up to a burned down house.
quote; 14/3 would be used for 3 wire circuits
Or a "split circuit", or a switched outlet on a duplex receptacle, or.........