Suppose I have asked a question and I have received answers but none are satisfactory. I get some thoughts regarding the question, including but not limited to a partial solution, later on. In such a case should I edit the question, add a comment, or ask an entirely new question? I fear that I shall be duplicating if I add a new question and if I edit the question the viewers who have already seen the question won't be supplied with this new information. Could I get any help here? Thanks very much.
It depends a bit on how much the edit changes the question. Ideally, edits to a question should not invalidate existing answers; if an edit would be that rigorous, it would be better to ask another question (also explaining why it's different from the original question). If not, you should just edit the existing question and place a comment on the answers that are already there, asking the authors politely if they want to have a look again at your edited question. They are the most likely to have a solution to your edited question too.
and if I edit the question the viewers who have already seen the question won't be supplied with this new information.
That's true, but they might not see your new question either. So that doesn't make posting a new question a better option.
In any case, you should avoid having your question become a chameleon question. That's more common on the programming and tech support websites than here, but it's a real problem.
After getting some answers, I think that, in some cases at least, you should add something like “Added note:” followed by the new thoughts that you had.