In a debate, what's it called when you pretend to agree with a point you don't actually agree with, because you think it will make the person more open to agreeing with you on other points?

I doubt it has a formal name as that's more of a psychological play rather than exclusively a debate action.

The only thing I can think of that is sorta related is called the foot-in-the-door technique. You're meeting someone halfway so they'll be more open to your position.

Arguing in bad faith?

I don't think it's bad faith. You're conceding a point to make the rest of your argument stronger.
- I’d call it lying to obtain an audience.
  
  In bad faith here could mean that you’re not in the debate to clarify the truth, but to manipulate others’ beliefs.

Strategic concession? Or just a compromise, really, but stretched out over a long play.

If presented in an honest way, it can be a form of open-mindedness.

I’m not sure how to say it more gracefully, but it could be something like:

I’m willing to grant that assumption even if I don’t believe it, in the context of this conversation, in order to explore the implications of that assumption.

Sort of an application of the scientific method, in combination with an acknowledgement of how the unconscious works in regard to mental resources. People often won’t really think about something seriously unless they believe its real. But in order to test a scientific theory one must use it to generate predictions.

So sort of pretending something is true, pretending you believe it even if you don’t believe it, could be a way of activating all the resources of your mind to explore where it goes with the implications.

I guess one way to put this from the other person’s perspective is to say “Humor me for a second. Let’s say that …”

Not very far from maieutics, the Socratic cooperative argumentative dialogue "based on asking and answering questions to stimulate critical thinking and to draw out ideas and underlying presuppositions" (Wikipedia).

It is less that you agree with a point of view then you asking questions in order to "bring out definitions implicit in the interlocutors' beliefs, or to help them further their understanding" (Wikipedia still).

You do not contradict them outright, you bring them to either contradict themselves, or to realize that their point of view is based on irrational beliefs and ultimately they change it.

You do not contradict them outright, you bring them to either contradict themselves, or to realize that their point of view is based on irrational beliefs and ultimately they change it.

Ha! I see you've never argued with conservatives. They'll contradict themselves a dozen times in one sentence. Then stand there proudly as if they made you and anyone around instantly change your core beliefs.
- I'm sure they had conservatives in Ancient Athens. You might need a great deal of training to pull it.
- It's not unique to conservatives. I've argued with people on all sides who were incapable of critical thinking.

Manipulation.

I usually call it sarcasm

The title of the question is worded in a way that I will assume we already know the position of whoever we are debating. If not, how could we else pretend to agree with their point?

So, we have two opposing views:

You know that I believe A to be true
I know that you believe B to be true

Then it is neither manipulative or in bad faith to "try on" the opposing view. How else can we learn more, if we are not open to understand or empathize? To answer your question, it's called being the devil's advocate:

a person who expresses a contentious opinion in order to provoke debate or test the strength of the opposing arguments. "the interviewer will need to play devil's advocate, to put the other side's case forward"

I feel like devil's advocate is the opposite. It's taking the opposite stance you truly believe in order to debate someone you agree with. OP seems to be asking more specifically about taking a stance you don't agree with to argue against someone you disagree with.

I'll be honest, if someone was doing that to me, and I figured it out - eventually the contradiction will get teased out as you dig into what they're saying - I would call it "bullshit".

If someone is going to compromise their statements as an attempt to manipulate my state of mind into agreeing with them, then they've shown complete contempt for my ability to understand them by sabotaging my ability to even know what they're saying, and I'd pretty quickly write off any more efforts to understand them. Maybe they've got something worth understanding, but if that's true then presumably someone else more capable and willing to speak their own mind can explain. The first person has proven themselves an unreliable source on anything.

Here's a question for anyone that does this: if you feel the need to lie about your position to make it sound reasonable, what does that say about your position? Maybe it's not actually reasonable? Maybe if you don't believe you can defend your position on its own merits, you don't even really understand it yourself?

I also have been thinking about this specific manipulation ability! Please let us know if you find out a term, I've been calling it social judo

Devil's advocate?

Playing devil’s advocate is done in the open; OP is describing something more covert.
- And it's when you present an opposing position.
Bingo