As per my experience, normally 2 seats are released and sometimes they may end up releasing more shortly before the flight.
One time, when I was IB Plat (not any more as I moved the BAEC) I gave them a ring and they allowed me to book one when there was no availability. It happened ballpark 2 weeks before the flight was scheduled: I had a paid J ticket and I wanted one for my companion to join me (the business cabin was pretty empty - mid Jan 2022 ORD-MAD)