Can one purchase extension to Apple Care plan

That is my understanding based on the following from Extend your AppleCare+ coverage - Apple Support

If you paid upfront, you can purchase coverage on a monthly basis after the 24 or 36 months is over.

but it isn't clear, especially how long after it expires that you can do it. I would try maybe a week before and if that doesn't work a day before, a day after, etc.

See the following, Extend your AppleCare+ coverage - Apple Support

You posted this question in the MacBook Pro forum. AppleCare+ cannot be extended on Macs, only on iPhones/iPads/Apple Watches which is why the linked article refers to iPhone, iPad, or Apple Watch coverage only.

If you have AppleCare+ on a Mac, you are limited to the original 3-year term and it cannot be extended.