Warranty Extension

Here is Apple’s current policy: Buy an AppleCare plan - Apple Support

The relevant section:

In most countries and regions, you can buy AppleCare+ within 60 days of your device purchase. In Japan, you can buy AppleCare+ within 30 days of your device purchase. In China mainland, you can buy AppleCare+ on your device within 7 days of your device purchase or in an Apple Store within 60 days of your device purchase. (At the Apple Store, you'll need to bring your proof of purchase, and we'll inspect the device.)

In some countries and regions, you can buy an AppleCare Protection Plan within 1 year of your purchase of an eligible Mac, Apple TV, or other device.

Contact Apple directly for more information.

You have 60 days from the original date of sale to add AppleCare+. After that, you can not do so.

That is not possible. You can not extend the warranty after the initial 60 days from the date of purchase.