TL;DR: Give the belongs on another site in the SE network option to normal users too, generating a moderator flag.
Often questions are posted on the wrong site on the Stack Exchange network (for volume reasons, most often at Stack Overflow). Then they need to be closed as off-topic, and optionally migrated to a better site.
The "close as off-topic" (or "flag as off-topic", if you don't yet have closing rights) dialog has up to five migration targets (the most likely migrations) build in, and if at least four of the five closers agree on one of them, the question will get migrated there.
Moderators see in this dialog actually one more option:
- belongs on another site in the Stack Exchange network
together with a text field which allows selecting a site by its name.
This option can be used to migrate a question to any site. We are normally using this only if it is either a really clear case that the question is on-topic at the target site, or we have asked a moderator of the target site. (Or a moderator of the target site has flagged the question at our site.)
Normal users don't have this option: They can only flag/vote to close as "off-topic", and use the "flag for moderator attention" general reason, and input a reason in the free-form text field:
Most of my flags in the last months on Stack Overflow are actually of this type (mostly for Crypto.SE and TeX.SE).
My feature proposal (actually, three of them)
Add this belongs to another site option to the GUI for normal users, too. Make this generate a normal "off-topic" close vote (if the user has close-voting rights, of course), together with a canned flag for moderators attention (which will be visible in the 10k mod tools).
(So such a vote will not generate a migration by itself, even if five users have the same idea.)
This should also be a possible flag option on questions which already are closed as off-topic.
On the moderator side, make it a tiny bit easier to decide about the migrations, and make them happen:
Show in the flag list if a moderator of the target site flagged for migration (these are "good" and need not be checked, other than for off-topic-ness on the source site). (E.g. show a diamond beside the name?)
If a question was flagged this way for migration, add the target site as an option to the moderator's close-dialog (so no searching is necessary).
(Allow migrating questions which are already closed as off-topic, without reopening.)
Related: Adapt close dialog UI for upcoming avalanche of StackExchange 2.0 graduates - Waffles' answer says such a search box was intentionally omitted so people don't have to do the hard work. So now moderators have to do this hard work instead (for cases other than the five ones listed). I'm not sure this is really better.