Last night I asked this question, of the form "if a function $f$ has properties 1, 2, ... does this imply that it also has property $X$?" The question as I posed it appears to have been fully answered (the answer is "no"). Over the course of thinking about the answer I realized I would really like to know the answer if I add a hypothesis about $f$. This would change the question to an essentially different one and (at least one of) the answers would no longer apply. So it seems rude to the answerers to directly edit the question. I could also add text at the bottom of the OP saying "EDIT: ...", acknowledging the answers and requesting further engagement. But I see two drawbacks to this. First, even though the question and answer currently found don't fully satisfy my own reason for asking, they are a complete question / answer pair, and maybe adding the variant would junk this up. Second, because the question has already been up for a day, perhaps the edit will not get very much attention. In light of this, a third possibility would be to ask a new question which is basically the old question plus the new constraint on $f$, and linking the old question. But this feels like junking up the site with near-duplicates. Have you faced a similar choice? What did you do and how did you think about it? And from the point of view of an answerer, which option do you prefer?
Way I see it, if an edit to your question is substantial enough that it would make extant satisfactory answers look incomplete/diminished, then you really should be asking a new question instead of editing your old one. If you ultimately take this route, a link to the older question would certainly be appreciated
cp'ing so we can have an "answer".