can i extend my applecare coverage period

Possibly. See the following from Extend your AppleCare+ coverage - Apple Support

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

Purchase the new coverage within 30 days after your original coverage ends. To find out if you can purchase the new coverage, go to mysupport.apple.com and follow the on-screen instructions. The new coverage automatically renews until canceled.

This is primarily a user-to-user support forum; other Apple users like you. Click on the following and see the information there: Extend your AppleCare+ coverage - Apple Support

Can Apple Care on my iPhone, which will be ended this month, be extended