The biggest question I would ask myself if I wanted to do so is:
"Do my changes affect the validity of any of the answers already given?".
If the answer to that is "yes", then I would stay away from the question. Especially in your case where you state "Well it invalidates the accepted answer, but not the most popular one."
But surely the users whose answer is now no longer (entirely) correct can adapt their answer to the new question? Well, they simply shouldn't have to. We already frown upon the OP of a question making their question a moving target. And I don't see why this basic principle should change for other users.
Sure, your intentions are good. But if you can't update the question in a way that leaves the current answers unaffected, I would simply advice you to ask your own question. If the relation to the original question is high or especially relevant, you could link to it in your own question.
Should your changes not be problematic in the sense described above, then you could consider the update. But even in that case I would personally be very cautious and honestly still ask my very own question to prevent any unforeseen consequences.