When I think of a story that changes it’s shape every time you read it, I think of a city; in particularly a city that one does not visit too often.
My example could be Christchurch, New Zealand, somewhere I frequent once or twice every couple of years. Each time I visit Christchurch, it’s story is evolving, whether it be through my grandparents moving house, or through the earthquake that devastated the city centre.
Each time it tells me something different about itself and this is the example I come to when I think of an ever-evolving story. It could be telling the story of the banding together and strength of the community in rebuilding the city, even using shipping crates as restaurants (a pretty cool idea if you ask me). It could be telling me the story of the brisk winter that is just ending and the warm summer ahead.
I would be intrigued by a story that changed its shape each time I looked at it, as it would mean that it was an active entity that you could never get sick of. It would be fascinating to be able to explore different outcomes like in those movies where you can choose your own ending.