Seven of Seven

Seven of Seven (七人のナナ, Shichinin no Nana) is an anime TV series created by Yasuhiro Imagawa (Giant Robo, G Gundam) and produced by A.C.G.T.
The TV series premiered January 10, 2002 on TV Tokyo and finished in run on June 27, 2002, totaling 25 episodes. A New Year's special episode was included in the seventh DVD volume (KIBA-745) released on October 2 of the same year. Due to production schedules, the manga adaptation, illustrated by Azusa Kunihiro, started serialization in Akita Shoten's Shōnen Champion on November 8, 2001, two months before the anime premiere. The manga ended on May 25, 2002 and collected in three volumes.
The title Seven of Seven or Shichinin no Nana is a pun, as the main character's name, Nana, also means 'seven' in Japanese. It relates the premise of the series, where Nana has split into seven different sides of the personality due to an accident with a crystal. In addition, Nana Suzuki's name is a reference to namesake Nana Mizuki, who voices the character of Nana in the anime.
The plots of the anime and the manga differ.
After seeing a rainbow as a child and being mesmerized by its beauty, Nana's grandfather has been trying all his life to capture the beauty of a rainbow within a crystallized form. After years of failed attempts and crazy inventions, such as a VCR toaster and vacuum cleaning mouse catcher, he finally discovers a way to make such a crystallized rainbow. His plan would work by separating the light from a rainbow into its seven basic colors and then reforming it into seven colorized crystals. His experiment was working too and only needed a few seconds in the microwave to be complete and finally fulfill his dream. That is when Nana, who was searching for the microwave in an attempt to bake a chocolate cake for Yuichi Kamichika (her crush), opened the door before the crystal had fully hardened and caused an accident.
The crystal glowed and split into the seven different colors of the rainbow, hitting Nana as one color and then coming out of her in the seven separate colors of the rainbow, creating seven different Nanas. Six different aspects of Nana's personality suddenly exist (acting to a more extreme extent) alongside the original in their own separate physical forms: there's a giggly Nana, a sleepy Nana, a crybaby Nana, a grumpy Nana, a flirtatious Nana, and an intellectual Nana. However, they're all still technically the same person, which includes Nana's crush on Yuichi. This is clearly seen when all the Nanas work together in perfect sync with each other (as if they're still just one person) to make him a chocolate cake for Valentine's Day. But once the cake is done, they immediately start fighting over who will give it to Yuichi.
Each Nana grabs one of the crystals that formed from the one crystal her grandfather was trying to harden in the microwave and realizes it gives her superpowers, she can fly, has super strength and super speed. This leads to a chase between the original Nana, and the new six sides of her personality who are all fighting as they fly and destroy parts of town over who will give the cake to Yuichi. But once they're finally done fighting, they once again prove that all seven Nanas are still the same person as they all find themselves too nervous to approach Yuichi and actually give him the cake.
The crystals also hold another power seen later on as Nana wears a costume from an anime series that she (and the other Nanas) loved as a child called the "Nana Rangers". While they are wearing the costume and at the same time carrying their crystals the prop costumes turn into the real "Nana Rangers" costumes allowing them at times to be Superheroes, and also all show themselves in public at once, since Nana and the others realize the danger of all being seen at the same time without some way of hiding that they're all the same person.
After they had settled on their roles, the 7 Nanas also face the fact that if the crystals aren't reintegrated within a year after the split, all 7 of them will disappear. Later, the 8th one appears causing chaos.
This story has no super power elements.
Nana Suzuki's father returns from a trip abroad, and he gives Nana a crystal that he had bought from a gypsy woman. He tells her the gypsy woman's warning, to never let the light of the moon pass through the crystal. That night Nana hangs the crystal in front of her window; there is a moon visible through the window. In the morning Nana wakes to find six other Nanas in bed with her.
Initially, Nana Suzuki goes to school and the other six Nanas stay home. The six quickly rebel against that plan. They take advantage of an opportunity to blackmail the principal of the school into letting all of them attend school, in the same class. The Nanas also quickly realize that it is confusing for all of them to be called "Nana", so they agree on nicknames for each of them.
Yuichi isn't the least bit bothered that there are now seven Nanas in his class. He doesn't show any favoritism towards any one of the Nanas over the others.
The anime set of characters. (The manga set corresponds with this to some degree)
Sgt. Frog's manga artist, Mine Yoshizaki, created the character concept designs for Seven of Seven. As such, various crossovers exist between the series. The character of Mutsumi Hojo, who appears as "Examinee 623" and the host of his own radio program in Seven of Seven, is a major character in Sgt. Frog. Melody Honey, a minor character in Sgt. Frog, appears and even receives a backstory. Additionally, the recurring ghost character in Sgt. Frog very closely resembles the design of the ghost that appeared in the temple in episode 12 of Seven of Seven.
In addition, episode 89 of Sgt. Frog features a plot that splits Corporal Giroro into seven personalities, most of whom resemble Nana's split personalities. A segment of the episode featuring Mutsumi takes place at the cherry tree seen frequently in Seven of Seven. In Volume 18 of the manga, a ninja named Nana is introduced. She looks identical to Nana from Seven of Seven. She also had six copies, each one with a personality matching the various Nanas from Seven of Seven.