Fantasy usability

Thought: it would be desirable that in im (and maybe not only in im) there was an opportunity to have several parallel conversations with the same interlocutor.
Everyone has happened to talk to a person about one thing . And flows, so to speak, the conversation evenly and consistently. Then you ask something , and then immediately something else , and more (and the person has not yet had time to answer your first question). Confusion often arises: what is the answer to which question?
Well, the familiar situation, huh?
So, the point is that in some way it was possible to separate these streams, so as not to be confused in thoughts.
For example: clicking a mouse on a replica of the interlocutor opens a separate window in which you can continue the discussion on this issue (with a mouse, of course, not very well, but it shows the essence). Accordingly, the other person makes the same changes in the window.
I hope at least something thought conveyed.
Maybe this solution is already there?

P. S. I am writing to a personal one, because I am not sure that thought is worthy of a thematic blog.