Collectors would then need to collect these pieces - either through some contests, random draws, treasure hunts, or even purely secondary purchases - and equip the parts into their puzzle.
Similar projects already exist:
An advanced version of this approach is a remake of the popular "one million dollar" website, or BAYC graffiti wall - one could make a single puzzle NFT into which others could guest-equip (a new RMRK functionality for temporary nesting) their pieces. This would allow for an interesting contest and collaborative experience in composing a single multi-user graphic wall, or could even expand to other media, like collaborative music compositions.
The original issuer of the parent NFT could then choose to "seal" the state of the wall at a certain point in time, disallowing withdrawals of the guest NFTs and finalizing the pieces into a piece of collaborative art.