When I try to flag a post, and try to mark it that it does not belong to this site, I only have two options to choose the other site to which the post should be migrated: Physics Meta SE and Mathematics SE.
What should I do if the post belongs to none of these, but to other sites like Cognitive Sciences SE? Should I then ask for Moderator Intervention?
I access the site from my smartphone, with user agent mobile.
Marking a question off topic and migrating it to another site are really two separate actions, although the system is not very good at making that clear. (Some people have been complaining about it for years.)
To notify the moderators that a question is a good candidate for migration to a site that isn't in the given list - which you should not be doing unless the question is also off topic, by the way - choose in need of moderator intervention and write a message like "Off topic; may be suitable for migration to cogsci.SE". You can also leave a comment on the post suggesting that it might be on topic at another site, though that's mostly for the asker's benefit.
Don't just do this for any old question that seems to be about cognitive science (or whatever), though. Candidates for migration should be good, on-topic questions on their target sites. If it's just a bad or mediocre question outright, we will not migrate it. If it's not within the other site's scope, they will reject the migration, which we'd like to avoid. You should have some idea of the other site's scope, enough to think the question in its current form would plausibly be a good contribution there, before suggesting a migration.
I'm actually not sure whether the system will let you cast both of these flags on the same post. If someone with ~100 rep can try it out on a deserving question and report back, I'll edit this answer accordingly. But if it turns out you can only cast one, unless the question is a really good fit on the other site, I'd advise just marking it as off topic.
