We brief that we would stop above 100 knots if:-
- Loss of thrust, confirmed by 2 parameters, one of which may be external.
- Master Warning
- Blocked runway
- any reason we think the aircraft won't get airborne
We would also consider it for an ATC call of STOP.
I've flown with different SOPs, some where either pilot can call STOP, some where the FO just calls the fault, but the reject decision is always the Captains. Personally I think its sensible for the FO to call STOP and state why - this gives the Captain a good early heads up. Otherwise by the time the FO has said "we've got a light, its a red one, and it looks like we have an engine failure (or whatever)....." we are gonna be 20 knots faster and that bit further down the runway!!! Whereas if the FO says "STOP, engine failure" its a pretty easy quick decision for the CPT.
At speeds close to V1 you don't have time to do a full diagnosis, which is why we just brief those 4 items - they are all easy to spot and the decision is ingrained. Things that you shouldn't stop for have the Master Warning suppressed during the take-off run at high speed anyway (ie. if something you need for stopping should break on the T/O roll) because you are far better to get airborne, reduce weight if necessary, then come back in using the full length of the runway, or divert to a longer runway if necessary, having fully briefed and got the thing as sorted as you can.