Q. on Fallacy of False Dichotomy

Hello All,
Oftentimes, in a scenario involving the usage of the fallacy of false dichotomy, all it takes is a third option to disprove the false logic. However, is it not true that in the case an interlocutor is trying to go further and actually disprove the validity of the option his opponent was trying to prove in the first place, the mere presenting of a valid, third option does absolutely nothing in that regard? In other words, am I wholly correct in saying that when someone uses the fallacy of a false dichotomy, the presenting of a valid, third or more option just indicates that you can have more than one valid option but does nothing to negate the validity of the option the individual wanted you to initially be persuaded to believe in? I say this because the individual could readily just affirm the third option you presented while still holding on to his own initial, first option; provided they are mutually exclusive; which oftentimes can be depending on the topic of contention at hand.
Rather, the actual validity of that would have to be disproved on its own merits and not by just presenting more options than what the individual limited it to in its false dichotomy setup. I would love to hear your views on this oft-used dialectic.
Thanks in advance guys!