These specials don't add plot. They add time alone with people you've already fallen for. Each one is a small, private moment that proves the show understands what romance actually is: not the confession, not the kiss, but the texture of being near someone you love when nothing dramatic is happening. Watch these if you need to remember what it feels like when a character becomes someone you want to check in on, the way you'd text a friend just to say hello.
Six short extras accompany Amagami SS+, one included with each of the six Blu-ray volumes of that anime. They are brief bonus pieces rather than full episodes, and like the material they supplement they fall under romance, with an ecchi slant, for viewers who picked up the home video release.