I have had this problem a couple of times. I ask a question about a problem, get some good answers, then I have another question about the same problem, and I'm not sure what to do. I have thought about the following options:

1. Ask the question as a comment to an answer. This what I normally do, but sometimes the question I have has not really to do with a specific answer.

2. Editing question and add the new question about the problem I've tried this some times, but I don't really like it. Many times I get no response to the edit, and if people add a new answer to the new quesiton, the page becomes choatic. Some answer about the old question, some answers about the new question.

3. Opening a new question about the same problem. I usually don't do this, because I feel like I'm opening an duplicate question. I'm wondering if it is okay to do this.

An example is sometimes more clear than a thousand words. I couple of days I asked: Is $\mathbb{Q}[α]=\{a+bα+cα^2 :a,b,c ∈ \mathbb{Q}\}$ with $α=\sqrt[3]{2}$ a field? I got some good answer. An half hour later, I thought about another way to solve the problem, and I edited the question, but no responses. Three days later I found out that this other way to solve this problem is incorrect. But I thought about yet another one, and I want to ask if that is correct way to solve the problem. I'm not sure where I should ask this.

Probably the quickest way to clarify minor details, since it involves people already familiar with the question.

I would advise against editing a question which already has answers in a way that changes the scope of the question. Doing so makes answers which were correct and complete for the old question suddenly incomplete or even off topic. I'd consider this rather rude towards the authors of existing answers. I know that when this happens to a question I answered, I tend to be annoyed and often even roll back the edit in question.

Opening a new question about the same problem.

If you have trouble with a different aspect of the problem, one which hasn't been covered by the original answers, then it likely is a new question. You might even edit the old question in such a way that it actually focuses on the aspect you got answers for. That would reduce overlap between the two questions. Of course, links between the two questions are helpful, as is a clear statement as to how they differ in focus. I'd go with this third approach in all cases where your first approach is not applicable.

If it were me:

• If my question originally focussed on the part of a problem that I found confusing, the answer addresses that part of the problem, and then I discover a new part of the problem that confuses you, then I have a new question, and I would ask it separately. I would link to the old question to try and stop the new one from being closed as a duplicate, and so that people can see what I already know.

• If my question was phrased as the more general "how do you solve this problem?" with some context, then it seems reasonable that people will respond with sketches and hints designed to get me unstuck, based on the context I provided. If these don't work (in the sense that they don't allow me to completely solve the problem, even if they helped me with some aspect of it), then I would start with comments explaining this, to try and get some further hints or more details. If this doesn't work, I would probably post a new question, but one of the first kind, that asks more specifically about the exact part of the problem on which I am stuck. If I also thought it was necessary to edit the original question, I'd try to make the timeline clear (i.e. by writing "answers by userX and userY helped me with this part, but now I'm stuck here", etc.).

What is also true of me is that I'm unlikely to post questions of the second kind in the first place, but that's just personal taste.

Applying this to your question: Is $\mathbb{Q}[α]=\{a+bα+cα^2 :a,b,c ∈ \mathbb{Q}\}$ with $α=\sqrt[3]{2}$ a field? I would say that you should have opened a new question instead of editing.