From this question I get the impression that there is some agreement that single-word-requests should really only give one answer per post. However, this behavior doesn't seem to be enforced in any way. Should we be flagging, downvoting or commenting on these answers to encourage the correct behavior?
If there are many possibilities, all of which are equally viable, the question may be in danger of being too open-ended.
In that case, the appropriate thing to do would be to narrow the question. Place a comment on the question, requesting stricter criteria for the answer they're looking for.
Meanwhile vote to close, as @Kit Z. Fox comments. Select "Off-topic", then the following from the resulting menu:
Questions on choosing an ideal word or phrase must include information on how it will be used in order to be answered. For help writing a good word or phrase request, see: About single word requests
If the question is closed, the resulting informative banner provides useful links for writing good SWR questions. On EL&U and Stack Exchange more generally, closing a question isn't quite the same as discarding it, (that's reserved for question deletion, and even that can be reversed). If the OP then edits the question, it will be queued for review to be reopened.
Naturally, it can feel quite confronting to find that one's question has been closed. If the OP edits their question suitably in response to your (comment-) request to narrow the question, it would be nice to also retract your vote-to-close. You'll need to click "close" (as if you were going to close the question again) to access the retraction button.
It may be that some users aren't aware that it's better to post separately.
I have, through the years, guided several users regarding this, and now they post separately, and also limit to the most suitable 1 or 2 suggestions along with respective explanations, instead of listing all synonyms in one go.
Also, like Lawrence mentioned, if the question is actually inviting a list of answers, or if it's too broad, deal with the question first. Guide the asker on how to narrow it down.