The title says it all, a specific example:
If an edit is substantial enough to invalidate existing answers, then you're by definition asking a different question.
If you're asking a different question, then you should post it as a new question. Changing questions after people have posted answers is not particularly nice to the people who gave of their time to answer the question you asked initially, and such edits are fair game for being rolled back by the community.
If you're worried that the question may appear similar enough to an existing question that it may draw duplicate flags or close votes, then you should take some time to highlight the differences between the questions. This may be as simple as "I know about that other question which is linked to here, but that question is asking about X, while I want to know about Y".
The only real exception to this would be questions that have been put on hold before receiving any answers, and the edit is intended to fix whatever caused the question to be put on hold, so that the question can be reopened. Such edits are usually fine even if they are more substantial than what would be acceptable to a question that has already received answers, because there are no answers that the edit risks invalidating.
In the case of the specific question you're linking to, the user who posted the answer has specifically said that it's okay if you edit, but that should be treated as the exception, and certainly not as the rule.