Are you sure?
I want add a newer version with background music but I afraid to do it.
Viewing post in Can you edit your entry after the submission period is over?
Yes, mechanically: the entry is a link to your project, and itch serves whatever build is live when a judge opens it. My post-deadline fix landed straight away. Whether adding music counts as polish or as changing the entry is the call of the host, not itch, so ask them there. If it was mine I would push it: a 48h jam entry with music beats a silent one.