Suppose you could make a reply "private", meaning only you and the person you're replying to could see your comment.

Their reply to your private reply should be automatically private, effectively creating an isolated thread.

People who want to disagree indefinitely on some fine point could do so without creating a ruckus.

If anything especially worthwhile came up in the discussion, either party could easily just repost it as an ordinary public reply.

To discourage people from harassing each other with private replies, you should only be allowed to downvote them.

This would also allow people an easy way to say "Thanks" or "I agree" without having those comments pollute the top level space.