Seems all too complicated. An SOP that gives the first officer full responsibility to initiate a rejected take off as PF if he considers it necessary, has serious implications legally and for flight safety. Is the captain merely an interested spectator while this happens? The legal eagles would love it.
Some operators have a touching faith in the ability of their first officers to make instant right decisions and if that means they have the authority to order the captain to reject a take off for whatever reason, so be it. It is a recipe for disaster caused by confusion about who is running the ship at the time a decision to reject is made and then action initiated.
Some years ago, an Australian airline using DC9's had a policy of the first officer as PF retaining control of the thrust levers on take off. Shortly before V1 on a limiting length runway, the F/O saw birds ahead and aborted the take off before the captain could say a thing. There was nothing wrong with the aircraft but it blew tyres and had red hot brakes when it departed the far threshold into the over-run.
The company quickly changed the policy directing that in future the captain would retain control of the throttles for take off and be entirely responsible for the decision to reject or continue. As PNF the first officer could call a malfunction during take off and the captain could choose whether to stop or continue depending on his own assessment of the problem. To this day, it is my understanding that no Australian operator authorises the first officer to call "Stop" as a direction to the captain. This makes a clear-cut policy of command responsibilty.
In a similar vein some years ago a UK registered 737 operator was responsible for training Australian crews to take over the operation within Australia. The Australian CAA noted the UK operator required the captain to flare and land with both hands on the control column while at the same time the F/O was given the responsibility for applying reverse thrust. During a rejected take off by the captain, the same SOP required the F/O to be responsible for reverse thrust in the abort.
The Australian regulator made it clear it did not approve of this splitting of responsibility saying it could lead to confusion especially on a slippery runway where modulation of reverse thrust in a crosswind may require instant action.
The Regulator maintained it was normal Boeing recommended procedure for the landing pilot to apply his own reverse as necessary and that a rejected take off required the captain to take over control and handle his own reverse as necessary.