The third season of Kyoukai no Rinne.

High school student Sakura Mamiya and impoverished death god Rinne Rokudou continue to confront the supernatural. Pulled into the problems of their quirky acquaintances, the pair again find themselves immersed in trouble. Ageha's black cat Oboro seeks revenge for alleged mistreatment and demands Ageha to nullify their contract. When she refuses to do so, a bitter quarrel breaks out between them. Meanwhile, the scheming Damashigami Company shows no sign of halting its wrongdoings, and the bat-like demon Masato continues to commit devious acts to pursue his long-awaited revenge on Rinne. For Sakura and Rinne, these paranormal complications never seem to end. As their saga continues to unfold, they must cope with these unusual circumstances as they appear, all while facing problems of their own. [Written by MAL Rewrite]

Saiga is a normal high school student with a gift in mathematics. His daily routine is disrupted when his family gets news that his Father's remains have been discovered—a noted archeologist and researcher who had gone missing while exploring a site many years before. Among his remains were notes and artifacts that needed to be identified by the family near a notable triangular mountain in Japan known as "Japan's pyramid", a place suspected by some to be man-made. A meteor containing a strange robotic lifeform falls from the sky and begins to cause destruction, putting Saiga in danger and causing a mysterious bracelet from his father's research to activate and merge him with an ancient robot burried within the pyramid—a robot the runes describe as Reideen. It is now up to Saiga and guardian Reideen to fight against this unknown alien threat from the sky. (Source: ANN)

Hibiki Amami would be a regular high school girl if it weren't for one thing: a sixth sense that allows her to see ghosts. Rather than being scared, Amami is more interested in befriending and helping the apparitions. This often leads to her human friends witnessing paranormal activity as the ghosts try to help Amami with everyday tasks. The majority of Amami's friends accept that she has a sixth sense, but Narumi Inoue—a girl who is terrified of the supernatural—refuses to acknowledge that ghosts are real. Though she is scared and stubborn, Inoue goes along with the rest of her friends, who decide to take up Amami's mission of helping ghosts however they can. [Written by MAL Rewrite]