High school student Emi Kaido receives a mysterious package containing an oversized pencil labeled as a Possibility Pencil, said to grant any wish. After testing its power to summon a missing lunch, she soon finds herself caught in a convenience store robbery. In desperation, she uses the pencil to draw a request for heroes, which unexpectedly summons legendary defenders from other dimensions. Ken Washio, the heroic Eagle Ken of the Science Ninja Team Gatchaman, appears first, quickly followed by the cyborg warrior Casshan, the vigilante fighter known as Hurricane Polimar, and the armored hero Tekkaman. These four heroes are now stranded in modern-day Tokyo and begin living alongside Emi. Ken poses as her uncle in her apartment, while the detective in her building secretly operates as Polimar. Casshan appears as a young cyborg, and one of her teachers is Tekkaman. Emi must now figure out how to send these displaced champions back to their home worlds while also understanding the true nature and origin of the pencil that brought them together.

The story is set in contemporary Tokyo and revolves around Emi Kaido, a mechanically inclined high school girl living alone while her father works abroad. The four heroes come from different classic Tatsunoko Productions franchises, each with their own established backstories and moral codes, leading to clashes in philosophy, particularly between the more idealistic Gatchaman and the lethal force-using Polimar. The Possibility Pencil operates on a logic-based rule: it can only create outcomes that are reasonable and plausible, preventing Emi from simply wishing problems away. The heroes gradually learn that their arrival is linked to a larger conspiracy involving a mysterious new drug called Anathema and an organization named Para Bellum, whose plan has the world racing towards destruction.

As the narrative progresses through multiple arcs, the team begins to settle into their unusual living situation. An early arc involves a drug ring distributing Anathema, which serves as a catalyst forcing the four heroes to work together despite their differences. A subsequent arc sees people begin disappearing throughout Shibuya, including Emi's friend Masumi and two of the heroes, Casshan and Polimar. Although Masumi eventually returns, she appears fundamentally changed, suggesting a deeper threat. A villain previously thought vanquished also resurfaces to confront the remaining heroes. The later story arcs escalate the conflict as the heroes continue investigating Para Bellum's attacks. One of their ultimate foes appears in Tokyo with the intention of revealing to Emi the truth about the world and her own identity. Following a major attack, the concept of heroes becomes widely discussed among Shibuya residents, drawing unwanted attention including from a tabloid reporter determined to unmask one of them. The team must also face Buraiking Boss, Casshan's greatest nemesis, who reveals that the dimensional crisis is more complex than they realized and that the evil force was not truly defeated with Para Bellum, indicating that the fight is just beginning.