The problem is of course what happens if there is a disagreement and a subsequent overrun.
There can be four Captains on our flight deck (including the DFO and Chief Pilot in the back) but neither they nor the LIFUS pilot in the left hand seat can command a reject. The commander who signs the tech log can delegate authority but not responsibility. Boeing define the high speed reject as a “critical phase of flight” and whilst anyone can identify the problem only one can make the reject command decision.
This is not a question of whether the LHS command trainee is competent but he is line flying under supervision. There can only be one command decision maker. As soon as the trainee passes his line check he has that sole responsibility once he has signed the tech log (with the exact same crew complement).