A320 TRI/TRE for a European legacy.
The following is our SOP: CDR has sole authority to call STOP/GO. LHS pilot (generally CDR) is responsible for the execution of the RTO. However, if the F/O is PF, then he/she is setting the thrust levers to FLX/TOGA/DTO and has responsibility for thrust levers at low speed reject up until LHS pilot calls "thrust set", at which point LHS pilot has his/her hands on the thrust levers (up until V1). We do operate a lot on really slippery runways and this procedure works fine.