Can an NFT be modified?

This is more of a food for thought to see if this idea would be desirable, or even possible, than a proposal. At the current stage, NFT's are not modifiable. But, only because our current consensus came to such a conclusion. But, technically if our consensus is to allow the modification of an NFT, then it should be possible, right?

One might ask, why would we modify an NFT? I'm just contemplating about what it means to own a digital item. An ownership could be like owning an art piece in the museum that we can never modify or it could be owning something that we could do whatever we want with it because, well, we own it. But, where does a digital item stand? Can we do whatever we want with a digital item we own and still maintain its unique identity? (Not just from the collectible standpoint, but from a supply chain to real estate, etc)

Basically, my question is, would the version control of an NFT be possible in the future? Usually an NFT is a token representing something like an image. The reference to the image is the SHA-256 digest of the image itself or the URL pointing to it stored on chain. It's stored in the mapping property of a contract, an owner to the NFT mapping.

This is a very crude concept, but let's say you hash the modified image along with the original image, create a mapping of a mapping that shows the relationship from an owner to the original image to the modified image, sort of like a hierarchical tree, would this be considered a modifiable NFT?

I guess this isn't really changing the consensus, but I'm just imagining what would happen if something like this were to be built into the ERC standard.