Interesting discussion this. Surely the most important thing is that everyone is clear who can say what during the t/o roll. In my airline (I believe on every fleet) the FO can call STOP (whoever is handling) for 5 reasons.
Any fire
Confirmed engine failure - 2 parameters
T/O config warning
WINDSHEAR AHEAD warning
MONITOR RADAR DISPLAY warning
Additionally, when handling pilot, the FO can call STOP for a blocked runway or significant handling difficulty. If they are handling, the FO carries out the reject and the Captain takes control as the aircraft comes to a stop.
If there is a P3 on the jumpseat, he can call what he sees but is not supposed to call STOP.
If unable to rotate the aircraft at Vr when handling, it's surely safer for the FO to reject than to advise the Captain and wait for him to make the inevitable decision. IMHO