One has to read the "fine print" carefully:
In Australia, Canada, Germany, Japan, the United Kingdom, and the United States, you can purchase the new coverage within 30 days of the end date of your original coverage.
Today is 18 Jan. My Applecare+ will expire on 16 Feb. From my perspective I am "within 30 days of the end date".
However, after a 15 minute chat; 15 minutes waiting for a scheduled call back; 20 minutes waiting for the support tech to look into the situation further; 5 minutes of very carefully rereading the document above.
IT APPEARS that one must wait until after the expiration date to update coverage.
Anyway, that is what the technician stated. We had a somewhat heated discussion about it while I re-read the support page several times.
"within 30 days of the end date" can be interpreted to mean before the end date or after the end date.
IMHO though, expired means expired and I have little faith that I will be successful on 16 Feb in extending coverage.
I am not a happy camper.