Is it possible to add a tool that shows mods all posts on the network that have at least one vote to migrate to their site? For example, a page SO moderators can see that shows all posts on the network where at least one person has cast a "belongs on Stack Overflow" vote. In this mockup, there are two posts waiting to migrate to UL; the first has 3 "belongs on Unix and Linux" votes and a 4th in some other category, while the second has only one migration vote and two others in some other category:
This sounds similiar to Can there be a feature for moderators to "reject" a question migration? and Require migrated questions to be accepted by the destination site's moderators, but flips the responsibility around -- mods can preemptively reject a migration before it happens, versus needing to manually approve every migration (which forces posts to stay in limbo until a mod has reviewed them). This behavior already happens manually; mods spot a post on SO that has migration votes when it doesn't actually belong on their site, so they find an SO mod to close the post before it gets enough votes. It seems like they should be able to handle it on their own -- when the post gets 5 votes it just closes as "off-topic" instead of migrating. If the post gets enough migration votes and a target site mod hasn't said anything, it migrates normally as it always has
In the mockup I also added an "approve" button. The intent was to let mods say "we'll take it now, there's no need to keep voting", but that basically lets mods steal a post from another site as long as it has 1 vote, so that might not be a good idea. The two features are independent though; "reject" can exist without "approve" (and actually, just a list with no buttons at all would still be better than nothing)