My AppleCare is expired, can I purchase it again?

See the information in Extend your AppleCare+ coverage - Apple Support

including the following excerpt:

• In the United States, if you paid upfront for an AppleCare+ plan for your Mac, you can purchase new coverage that renews annually. 

See the following from the same link previously provided:

Purchase the new coverage within 30 days of the end date of your original coverage. To purchase the new coverage, go to mysupport.apple.com and follow the on-screen instructions. The new coverage automatically renews until canceled.

If it expired longer than 30 days ago, I don't know if Apple will make an exception. There is a Contact Support link at the top right of this page if you want to try.