I may not even know if I have a composer “complete” because I’m lax in the checkbox department.
I’m pretty sure I have all (or close to all) compositions (by no means all recordings) by:
Gustav Mahler
György Ligeti
Pierre Boulez
Richard Wagner
I do have so many Jerry Goldsmith scores, I might as well strive for completion now…
As a side note:
I also have all Duck comics by Carl Barks, the one collection I started and finished with the completionist’s mindset. 🙂