Is it possible for users with 3000 reputation to vote to migrate a question to another SE site? If not, is it possible for ♦ moderators to do so?
For 3k users: Partially.
Users are only allowed to vote to migrate to sites that have shown a need for it. In our case, the only site users can vote to migrate to (besides our own meta) is Stack Overflow:
We haven't migrated enough posts anywhere else to warrant adding migration paths for them, but that can always be reconsidered in the future.
For ♦ mods: Yes.
On the rare occasion where you do see an off-topic post that belongs on another site, vote to close as off-topic and flag for mod attention. Mods can migrate the post to any SE site (including betas). If we start to see a pattern of migrating to the same site frequently, we'll try to get a migration path there so 3k users can handle it directly