Move a post out of a forum they have rights to (delete from forums index).
Move a post into a forum they have rights to (add to forums index).
Move a post between any two forums they have rights to (a combo add + delete op).
A message could potentially be posted whenever these operations took place by a specific bot account. These bot messages would be injected with a special display showing moderation actions within the thread at the appropriate place in the timeline.
Allow mods/owners of forums to:
A message could potentially be posted whenever these operations took place by a specific bot account. These bot messages would be injected with a special display showing moderation actions within the thread at the appropriate place in the timeline.