I had a bad conversation the other day; the sort in which you and the other person are talking at cross-purposes. We agreed far more than we disagreed on the subject, but he was so surprised that I disagreed at all that he kept returning to the difference.
In retrospect, I should have said, "Time out. I propose that we erase everything we've said up to this point. Can we start over again with a blank slate?" We then could have proceeded by focusing on the central subject.
That might have worked because the disagreement was not over a fundamental or crucial point. It was on an issue which was irrelevant to the purpose of the meeting.
There is certainly no guarantee that the tactic would have been successful, but it would have been worth the attempt. We finally got around to the areas of agreement but the detour consumed a lot of time. It was not a waste of time, however, because the experience provided one more lesson in the perils of communication.