Can I renew AppleCare after the first 3 years?

That will be up to Apple.

Extend your AppleCare+ coverage - Apple Support

Shamur wrote:

My AppleCare is about to expire after 3 years. Can I purchase a new plan for another 3 years?

Only by purchasing a new device.

Read the link babowa posted. It has been an option to extend AppleCare plans for a while now.

lobsterghost1 wrote:

Read the link babowa posted. It has been an option to extend AppleCare plans for a while now.

That's interesting. Thanks for letting me know.

You're welcome. Makes sense the plans can be extended. Added revenue for minimal use.

Thanks!