Can the back tail of an airplane move the neutral point backwards?
Yes you can, the tail volume needs to be such that the neutral point shifts aft of the CoG. This answer has some details - positive lift from the tailplane, but it must never stall!

More details about tailplane design in the answers to this question. The absolute safest config at a wide range of CoG is the CoG in front of the Centre of Pressure of the main wing, and a downforce from the horizontal tail.