Purchasing Additional Applecare Coverage

Hello!

I recently received a new macbook and am being prompted to purchase AppleCare+ within a time limit. However, the computer is already covered by a 1 year warranty. My previous macbook did not prompt me to purchase within 60 days of receipt, but rather within another time limit (don't remember how long) after the default AppleCare warranty expired.

Is there no longer an option to purchase AppleCare coverage after the manufacture's warranty period, or do I really need to purchase an additional warranty on top of the manufacturer warranty if I want to ensure my device is covered passed one year of use?