An attack delivered with an attack on the blade followed by a simple attack can be met in a number of ways. The fencers who is attacked can:
(1) open the distance, allow the attack to fall short, and take over the attack,
(2) deceive the beat by derobement, followed by a straight thrust,
(3) parry by beat parry of the final attack,
(4) change parry off the beat, or
The counterattack response to the beat varies by weapon, largely driven by the character of the target, the line of the attack, and lock-out time.
The weapon in which this answer to the attack is easiest is in epee. The beat is answered by an immediate replacement of the blade with the intention of hitting the advanced target, accompanied by control of the distance (usually a retreat) to ensure that lock-out of the original attack will occur. If the intent is to provoke a double, it is worth experimenting with a lunge with the replacement.
Sabre also allows the counterattack on the beat. In this case, it would seem that the counterattack has the greatest chance of success if executed with step or jump back and the cut delivered on the advancing arm.
In foil this action is more problematic because you have to (1) avoid being hit during the opponent's right of way and (2) get to the torso with the counterattack. This suggests that you need one light, and the best way to get one light may be a time hit closing the line rather that a stop hit.
Just like in any stop hit, your chances of success increase significantly if:
(1) the opponent commits a fault in the delivery of the attack, a beat followed by a delay in extending on the attack as an example.
(2) the opponent has an accuracy problem. If your opponent misses the target on a significant percentage of his or her actions, the stop becomes a predictable risk-benefit calculation.
(3) you seize a psychological moment and cause the opponent to abandon his or her attack as you hit. Against well trained opponents this happens rarely, but it does happen.