Re: "Extending AppleCare for Apple Watch SE"
We are all Apple customers. just as you are, so we can't speak for Apple or Apple Care ... it may also depend on your country or region, and the condition of the watch etc.
There is some info. on checking watch eligibility in the article below:
Check device eligibility for AppleCare coverage - Apple Support
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Also: Linked article below says:
" If your AppleCare plan for your Apple device expires, you might be able to purchase new coverage within 45 days after your coverage ends. Your new plan will have recurring payments."
Please choose your country or region in the article below:
Get AppleCare coverage for your Apple device - Apple Support
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For more info:
Contact or Visit Apple Support
or
Use the Apple Support app
or
There's support and contact options on the Watch Support website:
Apple Watch - Official Apple Support