Maximum speed during takeoff at which a pilot must first make an action to stop the aircraft within the accelerate-stop distance. May also mean the minimum takeoff speed that will allow the pilot to continue the takeoff after failure of a critical engine.
This quote is the "key"

The answer depends on whether the V1 you have is "go V1", or a "Stop V1". Traditionally, and in the majority of the posts above, a "Stop V1" is assumed i.e. a reject > V1 almost guarantees an overrun which is v dangerous.
However, frequently "we" fly to a "go V1" e.g. a light A319 off LHR with a V1 of 115K

You could get off LHR, climb to 300', then land back on and stop

The problem is you rarely know what type of V1 you have, and even if you did, how far beyond it you can go before it becomes the other type of V1
So in round terms you have to treat it as a "go V1", and even in the scenario above, I will "go" for an engine failure > 115K with 10,000'+ remaining - that is the only "correct" action. But, in a complex / multi failure situation, a "stop" might be called for, that is what "judgement" is, and what we are paid for. NB it is not "incorrect" to reject > V1, just the circumstances in which it is warranted are not defined
NoD