How to implement fractional ownership with existing standards

I'm trying to implement "shared ownership" of an ERC-721 contract (NFT) that is split into ERC-20 tokens that represent "shares". From a high level perspective, how could I go about doing this?

I was thinking about making an ERC-20 contract that owns an ERC-721 contract - thus the tokens would "own" the NFT and people can buy the tokens to partially own the NFT. Would this be feasible for a marketplace?

I looked into ERC-1155 (contract that combines ERC-20 and ERC-721) but I'm not sure how the token and the NFT would be related. Any help would be much appreciated.

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