Midarezaki Ouka is used to having strange things happen to him -after all, he is the head of the Great Japanese Empire Paranormal Phenomena Bureau of Measures. But when he catches a small cat girl in the shopping district stealing apples, his whole life rearranges to fit a new operation... OPERATION COZY FAMILY. Thousands of years ago, Enka the God of Destruction, was killed. However, with a dying breath it claimed that its child would appear and destroy humanity. Now in futuristic Japan, all of the potential children of Enka have been found and placed into a haphazard family. Teika the lion, Gekka the jellyfish, Yuuka the oni, Ginka the cross-dressing mafia son, and Hyouka the bioweapon--along with their parents Ouka and Kyouka (the ruler of a demon underworld)--all live under one roof in a family frenzy.

Professor Layton's daughter, Katrielle Layton, runs the Layton Detective Agency together with the talking dog Sherl and her assistant Ernest, and solves strange cases that happen everyday in London. Originally, she started the job with the purpose of finding her father, Hershel Layton, who had disappeared suddenly, but her incredible ability to solve puzzles made her well-known and she receives numerous requests.

The story of the mecha anime revolves around 13-year-old Meguru Tokio, who is suddenly approached by a strange woman who is running away from something. She finds out that the girl's name is also Meguru, and although she appears to be around 17 or 18 years old, she has a passionate personality, which the younger Meguru has trouble dealing with. Meguru Tokio gets drawn into the older Meguru's fight with a mysterious organization, and gets targeted by the organization as well. The one targeting them from the organization was the narcissist, Rei. Although the younger Meguru can't believe that the older one came from the future, she fights alongside her in a dimensional robot. After fighting with Rei, she finds out that even though the other Meguru is older than her, she is Meguru Tokio's descendant. After finding out that someone has jumped into the past by the older Meguru's history surveillance device, the two also make a leap back into the past.

Not long after forming their partnership, detectives Ron Kamonohashi and Totomaru Isshiki have proven adept at solving various cases together. However, the two are further motivated to continue their work when they discover that the House of M—an infamous crime syndicate—orchestrated Ron's expulsion from the prestigious Detective Training Academy BLUE five years prior. It appears that this group is also linked to Ron's mysterious ability that causes those around him to lose their lives, a phenomenon which Ron is desperate to stop. A member of the House of M soon starts to commit boastful serial murders around Shibuya as an act of provocation toward Ron. Consequently, the investigative pair must do their best to apprehend the culprit for the sake of justice as well as learning more about Ron's dark past and present condition.