The last option situation for the attacker comes when the opponent decides that the best answer is a counteroffensive action: stop thrust, stop cut, or time hit (the stop action with opposition or interception). In this discussion we will work from the assumption that you, as the attacker, intended to hit with the attack, not draw a counterattack for the purpose of countertime (defensive, counteroffensive, or offensive) or counterattack in tempo. This is not to say that the counterattack should catch you by surprise - counterattacks are a key part of any opponent's skill set, and you must be prepared to deal with them.
The tactical opportunities for counterattacks are best in epee, as there is no concern for right of way. In addition, the double hit allows the counterattack to be used to achieve distinctly different objectives. To understand how, we first have to understand the double hit. The epee rules allow for a double hit whenever two touches occur within 1/25th of a second (40 milliseconds of each other). This actually creates a window 80 milliseconds wide - I can hit up to 40 milliseconds before my opponent hits or up to 40 milliseconds after he hits. Although this is a short time window, it allows me to be either first or second with the touch and still create a double touch.
This allows the opponent to play the Epee game with subtlety:
... in the pools a double hit is generally not desirable if the opponent intends to win the bout - it increases your touches scored for seeding in tied indicator situations (thereby impacting both her and her teammates), while at the same time not providing her with an indicator increase,
... unless he is losing and expect to lose - in this case double hits maintain his indicator, and help his touches scored total, while preventing an increase in the yours. Never go into a bout expecting to lose, but if it is going to happen, fight to have your light on in every touch,
... in the direct elimination, because the amount you win or lose by has no impact, expect an opponent who is ahead to double touch to preserve the lead,
... and beware the double touch in 1 minute situations after time expires with the score tied - the double touch is ignored, so opponents have a real incentive to double hit to run down the clock, especially if they have priority.
The second most permissive environment is in sabre. The extended arm advanced target allows a fencer with good blade control and the ability to control distance to stop cut, or stop point, the extended arm of the attacker followed by a rapid retreat to time the attack out. The extreme example of this is the so-called "Skyhook" stop cut. This results in a single light in favor of the counterattacker. The importance of distance and timing in modern sabre also allows success in counterattacks into preparation or attacks with tempo problems.
Foil is probably the least permissive environment. Because the target is restricted to the torso, being faster or hitting a different target than the attacker does not gain your opponent either right of way or a lock out time advantage (except with referees who are just watching the lights and not bothering with the actual action). To succeed, the counterattack must clearly land in preparation, exploit a problem such as chronic inaccuracy, or close the line to prevent the original action from scoring.
As an attacker in any weapon, how do you deal with the counterattack? There are a number of possible solutions:
... accelerate the attack so that your action clearly lands first, preferably one light first. However, be alert to the possibility of an opponent making a false counterattack to draw you into a premature or a deeper commitment that he can countertime.
... parry the counterattack and riposte. In epee this should be done controlling the opponent's blade. In foil and sabre, speed would seem to be essential, along with a closing of the line or a final closeout.
... counterattack the counterattack in sabre or epee - the opponent's advanced target is coming forward, so relocate your aim point to take advantage of the opportunity. In sabre, this will look to the referee as though you are simply completing your attack and should retain right of way.
... pull distance (arm or body) if the counterattack is in your preparation, gain control of the opponent's blade, and hit with opposition.
... evade if the counterattack is high with a transition to a low line attack with a lowering of the body.
All of these require five elements: (1) nerve (you cannot hesitate or ponder consequences), (2) ability to rapidly recognize the situation, decide, and take action, (3) excellent blade and point control, (4) clean technique with an instinctive ability to cover your action, and (5) thousands of repetitions in practice. So start working now to develop this option in your attacking environment.