So! What I’d propose as a first attempt at this (to be improved in the future if necessary):
No new work types as part of this change (more work types should be added in the future, but not for “what kind of part something is” - just for “what kind of thing this part is”).
A few new attributes should be added to the “part of” relationship:
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Collection (Y part of collection: X, X collects: Y): wording could be changed but basically this would represent a case where the “parent work” is not necessarily meant to be performed as a set. For example, Brahms’ collection of 5 songs, op. 72, or Debussy’s second book of preludes, or Beethoven’s 3 piano sonatas, op. 10. Parts of a collection can still be ordered/numbered (and often are!) - it just doesn’t necessarily refer to the required performance order.
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Movement (Y movement of: X, X has movement: Y): a case where the parent work consists of several parts, which are generally meant to be performed one after another in a particular order. For stuff like Stockhausen’s Tierkreis or other (mostly contemporary) works were all the parts (or a specific number of them) should be played in a different order each time, I’d suggest not using “movement”, but sticking to a more generic “part” relationship.
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Act (Y act of: X, X has act: Y): for operas and similar works, in order to make it possible to know how many acts an opera has; this is often desirable information, but it’s hard for a machine to tell as it is since they’ll often also have other parts like overtures and entr’actes/intermezzos.
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Number (Y number of: X, X has number: Y): for operas and similar works that are separated in numbers. It would allow us to store the information about the numbers defined by the composers, even if there are (for example) spoken segments in between (like in Mozart’s Singspiel “Die Entführung aus dem Serail”).
If we see this approach works well, we might want to add other attributes for other uses, but this seems to be a small but useful starting set.