THIS link states that unless you purchased AppleCare when you bought the Mac, one can buy within 60 days of the Mac purchase. Not sure about monthly v yearly cost.
I picked up my iMac 24” from the Apple shop in Avalon (Alpharetta, GA), and during the pick up process, the Agent offered me the option to purchase the 3 year plan. So, I did.
They also advised that you can do the yearly option, and it will keep renewing, unless you cancel it, for up to 6 six years.
From my understanding, post the initial 3 year option of the Apple Care, I should be offered more options, up to 6 years…