Can I buy AppleCare if I still have 11 months of warranty remaining?

From: Buy an AppleCare plan - Apple Support

"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 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."

Again, here is how to: Buy an AppleCare plan - Apple Support

Follow that path, and—if available for your device, and for your location—purchase an AppleCare plan there.