If you liked the Kokoro Connect anime, the Anime-Planet community thinks you'd like:
Tomoya Okazaki is a third-year high school student who is generally bored with life and doesn't take his studies, future, or anything else seriously. One day, however, he meets a lonely-looking girl in the school courtyard, Nagisa Furukawa. She explains to him the source of her loneliness: she had missed a lot of the previous school year and thus is repeating her third year; everybody that she knew has already graduated, and she is lonely. Tomoya is rather indifferent at first, but decides that he has nothing better to do and spends increasingly more time helping Nagisa restore the school drama club. As his relationship with Nagisa grows, Tomoya begins to open up to various other people around the school as well...
Both of these shows show a group of friends as they learn more about each other, learn more about themselves, and learn how much they need each other's support as they go through various emotionally trying challenges. There is an element of the supernatural that is vital to each story, which helps give these shows a different feel from most school life animes. They have serious moments, humorous moments, and heart-wrenching moments, and if you liked one, you will definitely like the other.
Haruka Kotoura has had a psychic ability to read minds since she was born, but her inability to grasp that she's different has led her to be ostracized by every friend she's made. When she meets Manabe, she can't help but be surprised - when he's not imagining strange creatures dancing through the desert, the boy is a hopeless pervert and makes no attempt to hide his dirtiest fantasies. What's more, Manabe isn't driven away by Kotoura seeing his thoughts, and even goes out of his way to befriend her - seemingly because he enjoys thinking of the girl erotically and seeing her subsequent embarrassment! Before long, the once-lonely girl even meets other students who aren't pushed away by her abilities. Could this be the start of a normal school life, with real, lasting friends for Kotoura?
After having lived elsewhere for several years, Sana returns to the town in which he grew up in, and quickly begins to reacquaint himself to his surroundings and new high school. While there, Sana runs into his four childhood friends: Shuu, Shuri, Aoi, and Nanaka; but for some strange reason Nanaka gives him the cold shoulder. As he goes about his new daily life, can Sana rebuild his friendship with Nanaka while trying to deal with a troubling secret from his past?
Both Nagi no Asukara and Kokoro Connect involve a group of close friends that overcome various interpersonal issues including a love polygon. Though each story contains important supernatural(Kokoro Connect) or fantasy (Nagi no Asukara) elements, each show remains largely slice-of-life. Both shows are centered around character relationships and development.
Sorata Kanda has a real problem - he just can't say no to the cute face of a kitten! However, his lovely strays have finally landed him in trouble, as his dorm doesn't allow keeping pets. Given an ultimatum to get rid of the cats or move out, Sorata makes the mistake of standing up for himself and finds himself exiled to Sakurasou, the home of misfits the school doesn't know what to do with. Yet the more he spends time there, Sorata sees they all have their own incredible talents. None, however, enthralls him more than the latest arrival: Mashiro Shiina, a world class artist who is seemingly incapable of feeding or clothing herself! Since none of the other residents have a shred of responsibility, the onus of 'Mashiro Duty' falls to Sorata; what will become of Sorata and his latest stray, and will he ever achieve his goal of escaping Sakurasou?
Although those 2 series seem quite different at a first glance, both contain an interesting blend of comedy drama and romance; Kokoro Connect being more dramatic whereas Sakurasou more humoristic.
Those shows explore the relationships between a group of students and in spite of an unrealistic setting (supernatural in Kokoro Connect or a bunch of weird people living together in Sakurasou) the way those characters interact with each other and their response to the occurring situations seem quite real.
Both anime have touching emotional moments, if you enjoyed one you may want to try the other.