Suzumiya Haruhi no Yuuutsu, Charlotte Recommendations
Both center around a group of psychical-ability wielders who disguises themselves as a group of high-school students that take part on various activities, under the name of SOS Brigade and Hoshinoumi's Student Council. Both groups are composed of similar characters : socially-outcast girl who leads the group, reluctant MC and his cute little sister, etc.
Haruhi tries to find them to recruit them into her club, while Nao for the sake of securing them from evil scientists.
High school students with special abilities in a club trying to find more people with special abilities. Somewhat similar characters (Nao = Haruhi + Yuki, Yuu = Kyon + Itsuki). Baseball episode. Alternates between character-based slice of life and supernatural drama.
The overall tone and the supernatural aspects are kind of similar, even though Charlotte is a bit more serious.