So please tell me how you Go Around from Base Leg then?
By maintaining, or climbing back up to and then maintaining, circuit height; turning on to a final approach track at the appropriate point and flying along (but just to one side of) the Runway until it was appropriate to turn Crosswind.
Technically, by flying just to one particular side of the Runway, an aircraft could be said to be on the Dead Side of the Runway BUT it would never have left the circuit so would not need to rejoin and, at all times, would be conforming to the circuit pattern.