You can purchase additional AppleCare as long as you are within your initial 1 year AppleCare warranty period. However, purchasing additional AppleCare at a later date won't make the AppleCare start/end on a later date. It will still end 3 years after your initial AppleCare ends.
Source:
https://store.apple.com/Catalog/US/Images/apple_certified.html
(3) Can I purchase the AppleCare Protection Plan for my Apple Certified Refurbished Product?
All Apple Certified Refurbished Products are covered by Apple's One-Year Limited Warranty. For extended coverage, you have the option of purchasing the AppleCare Protection Plan with your Apple Certified Refurbished Product. The AppleCare Protection Plan extends the complimentary coverage on your Apple Certified Refurbished Product to up to three years of world-class support for Mac, and up to two years of world-class support for iPod, iPad, iPhone, and Apple TV.
https://www.apple.com/asia/support/products/faqs.html
You can purchase the AppleCare Protection Plan anytime within the one-year limited warranty period. Your eligibility for coverage under the AppleCare Protection Plan starts from your hardware purchase date. Apple strongly recommends that you purchase the AppleCare Protection Plan when you purchase your Apple product to maximize the additional benefits provided under the plan.