So there's steelmanning, where you construct a view that isn't your interlocutor's but is, according to you, more true / coherent / believable than your interlocutor's. Then there's the Ideological Turing Test, where you restate your interlocutor's view in such a way that ze fully endorses your restatement.

Another dimension is how clear things are to the audience. A further criterion for restating your interlocutor's view is the extent to which your restatement makes it feasible / easy for your audience to (accurately) judge that view. You could pass an ITT without especially hitting this bar. Your interlocutor's view may have an upstream crux that ze doesn't especially feel has to be brought out (so, not necessary for the ITT), but which is the most cruxy element for most of the audience. You can pass the ITT while emphasizing that crux or while not emphasizing that crux; from your interlocutor's point of view, the crux is not necessarily that central, but is agreeable if stated.

I proposed a term for this bar of exposition / restatement: ostentiate / ostentiation. Other terms:

• ekthesize / exthesize; phosphanize, epiphotize; elogize; anaply / anaplain; anaptychize / exptychize / eptychize;
• adluminate, superluminate; ostentiate, superostentiate;
• belight, beshine, enbeacon.

Mateusz Bagiński suggested:

Exoclarification? Alloclarification? Democlarification (dēmos - "people")?

I was going to go with "allophanize" for now (keeping it Greek): "make apparent to others". "Exophanize" also isn't bad.

"Allophanize" has two problems: "allo-" allegedly means "another of the same kind", where "hetero-" (another of a different kind) might be better, since we are talking about make our interlocutor's idea clear to someone who is not our interlocutor, which in this context is a very salient difference. But, allo- is also ok. They are both people.

The other problem is that it's ambiguous between "make appear to another", as we mean, vs. "make appear other / as another", which is a useful meaning but different.

Gippity suggests "prosphanize" meaning "make appear to". So we can say "heteroprosphanize" meaning "make appear to another of a different kind (someone who didn't originate this idea)". But, that is too long.

So for now I'll say: "alloprosphanize".