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 most obvious one that comes to mind besides The Melancholy of Haruhi Suzumiya is the movie duo of “To Every You I’ve Loved Before” and “To Me, The One Who Loved You”. In fact picking which movie to watch first ties into the plots of the movies themselves in a way.