A closure taking ownership of the closed-over variables doesn't actually imply that it is FnOnce (only callable once). You can perfectly well have a Fn or FnMut

A closure taking ownership of the closed-over variables doesn't actually imply that it is FnOnce (only callable once). You can perfectly well have a Fn or FnMut closure that owns its captures, as long as you don't try to do any moves inside the closure. If you need to do a move in an FnMut closure, you can also wrap the captured variable in an Option, and use .take()