IMHO MSE should allow to post a discussion type question, such that the discussion would continue in a specific chat room. The question should not be closed and a link of the chat room should be given in the question. The question can be tagged with a new tag,
After the discussion gets finished, the important points(results) of the discussion should be posted as the answer to the question. This way the main site will not become a discussion forum and many new things will be available for future users to know.
This way one would get enough attention of the many users which could be difficult in the main chatroom as Mr. Alexander Gruber points out in his comment. And some new important mathematical stuff will be available on the main site in Q/A format.
As an example one can see my recent question about rational numbers. I do not claim that its an excellent question, but it gets my point across. I had a discussion with a user and finally we got a convincing argument. I'm thinking to put the main results of our discussion in the question now(or answer?).