All right then, before the V1 call.
It should always be possible to reject a take-off before V1 - that's what it means.
But it requires prompt performance from a practised crew; and the closer you get to V1, the more important this becomes.
But rarely is V1 so limiting that an abort precisely at V1 will not allow the aeroplane to be brought to a halt on the RW/stopway remaining.
I must have initiated hundreds of fires/failures at V1 over the years (in the simulator, I hasten to add). Rarely did anyone screw up an abort disastrously - but they did have the luxury of at least 9 x 3 hour simulator sessions per year. Something which I doubt airline beancounters would ever allow these days.