Not that I am perfect at it or anything but the higher level of disagreement would be to not reflect the tone and use understatement in response to overstatement ("that's not quite true" vs "you are a liar") and to not carry any
particular point on ad nauseum. I think the latter is the main part though. If you were both tripping over each other in pleasantries ad nauseum there are still diminishing returns and at some point every horse dies.
If I find myself riding an ex-horse I usually try to excuse myself from the discussion ("I guess we'll have to agree to disagree, we seem to be repeating ourselves") in order to avail myself of a live one.
Of course I usually realize that right around this point anyway so I'm obviously not immune to getting caught up in a discussion that lives long past the point at which it is profitable to anyone but getting the last word in a circular discussion is a Pyrrhic victory and there is no dishonor in quitting an exchange that no longer edifies.