Can I add on another year of apple care plus coverage if my coverage is going to expire soon?

It depends on what level of AppleCare you have. If you have the standard one year AppleCare plan which came with your iPhone, that cannot be extended. If you purchased an AppleCare+ Plan when you purchased your iPhone (or within 60 days of purchase), in some countries, AppleCare+ plans can be extended on a month to month basis within 30 days of the plans expiration date.

See this --> Extend your AppleCare+ coverage - Apple Support