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 Magical Index series seriously weaves and overlaps in similar timeframes across three different series:
It’s so intertwined at points you can jump to another series to see what’s happening to that character at the same time as another character. I tried to put together a chronological watch order and got half way through it.