The first line of defense I would use in such situations is to look for win-win scenarios. While propositional logic and much of Western philosophy may love the Law of the Excluded Middle, I have found a surprisingly large number of debates admit some middle option, if you look for it. It is very rare that two individuals actually come into a debate with perfectly polar opposite viewpoints (unless this is an artificial debate, designed to promote the idea of a winner and a loser). If you win, who cares if they don't lose! Let them be happy too!
Finding such a state isn't easy, of course. I have found a few approaches that I find work well for identifying such a state when I am short on information:
- Let my opponent define the battlefield. If I'm coming into a debate without enough preparation, it's my fault. I am now obliged to use the only source of knowledge available to me: my opponent. This can only be done if I allow my opponent to say more than they intended to say. Go ahead, let them define abortion. While they're at it, see if you can goad them into saying something about the value of life in general. It wasn't directly on the topic, but now that's information I have that I didn't have before, and they wont challenge it, because it's their idea in the first place!
- Work with them in the flow of the debate, accentuating their directions.
- If they're using sharp formal language, sharpen it further. Make them define the exact meanings of words they are using. Eventually they must come to either an informally defined word, or a situation where you can apply something like Godel's incompleteness theorem or Tarski's non-definability theorem to prove they have to have a flaw in their logic. How do I know this has to happen? Cheating really... very few topics which can be described fully in formal logic become debate worthy! (And if they do succeed in defining it, then at least you came out looking okay... for the guy who had to argue the provably losing side!)
- If they're using loose informal wording, make it more informal. Try to rip axiom after axiom out of their argument until it can barely stand on its own two feet.
- In either case, their argument starts to be wobbly. Once its there, the dance begins. You need to pick up your partner, and lead them along until you arrive at an informal debate that you are comfortable with, and have enough preparation to survive. (not prepared for any debate? Shame on you. Waltz on. As long as everyone is enjoying the dance, they wont mind that you hijacked their debate and turned it into something else)
- Once you have taken control of the debate, build it up in a way that doesn't oppose your own viewpoints (and ideally actually supports your viewpoints). However, make sure that the final solution feels like a win-win to you and your opponent. If they walk away feeling like they accomplished something, nobody will mind that you totally B.S.ed you way through the entire debate. If you grind someone into the ground, they will feel offended, and will try to prevent you from using the same approaches next time.
Closing as I started, seek the win-win to the debate, and your opponent will have less of a reason to actually try to make you lose (which is good, because your opponent holds all the cards, since they prepared and you did not)