I’m interested to hear about anime that give a different experience when putting the episodes in a different order. They can be official orders (broadcast vs dvd) or fan orders (moving arcs around, putting seasons in chronological vs release order). Maybe you can even think of examples where a companion movie is inserted in the middle of a season? Two separate projects by the same author or studio that can be weaved together to form a consistent whole?
The Horimiya anime originally skipped a bunch of stuff that was covered in a later season, titled “Horimiya Pieces” or something like that. If you want to watch the events in the order they happened in the manga it’s a crazy mess.