Lagrange: The Flower of Rin-ne

As a girl named Madoka Kyono rescues a girl from drowning, she finds her school uniform missing and later returned by a strange girl. Later that night, Madoka is questioned by her sister about something. The next day, Madoka once again meets the girl, who introduces herself as Lan and asks Madoka to pilot a robotic aircraft at an offshore base. As Madoka touches the aircraft and experiences a flashback of sorts, a robot from outer space appears and attacks the base. Lan reveals herself to be an alien sent to protect Madoka and the aircraft, the two of which are linked together. Madoka agrees to pilot the aircraft, which responds to her emotions and changes into a robotic form to fight against the enemy robot, defeating it using Madoka's knowledge of club activities.

Madoka’s excitement over her triumphant victory is short-lived when she is told by Pharos officials to be ready for the next battle. Feeling like she’s been tricked into becoming a Vox pilot, a furious Madoka plans an escape.

As Madoka rushes to fight against the enemy Ovid to protect her town, Lan becomes conflicted about a legend Madoka doesn't know of, the fear of which prevents her from being able to pilot her own Vox Lympha. As the enemy, Kirius, tries to ask Madoka to come to her planet, she refuses and the fight resumes. Feeling Madoka is in danger, Lan overcomes her fear and pilots the Lympha, but finds herself up against the other enemy Ovid. As Lan expresses her guilt towards dragging Madoka into this, Madoka lifts her spirits, enabling her to overcome her fears and transform Lympha into its fighter mode, allowing her to come to Madoka's aid, forcing the enemy to retreat. Afterwards, Madoka and Lan decide to name their Vox units Midori and Orca respectively.

Muginami transfers into Madoka's class, which causes worry for the organisation. Later, Youko and one of the organization's representatives talk to Madoka's teacher about her piloting Midori. Youko agrees to let Madoka continue piloting Midori on the condition that she is allowed to continue living at home and attending school. Soon afterwards, Madoka and Muginami participate in an open swimming contest whilst Lan keeps watch on a boat. Spotting her, Muginami decides to play a prank on Lan and tip her into the sea, unaware that she is unable to swim. Realising her mistake, Muginami helps Madoka rescue Lan and performs CPR on her. Afterwards, Madoka invites Muginami to join the Jersey Club, much to Lan's annoyance. Both Muginami and Lan decide to help out at Madoka's family restaurant, with their individual traits attracting many customers. After becoming jealous after Madoka allows Muginami to live with her, Lan also decides to transfer into Madoka's class, join the Jersey Club and start living with Madoka. Meanwhile, a glitch in security allows Array to escape imprisonment and rejoin his allies, who are making a deal with another enemy.

A man named Villagiulio comes, who Muginami reveals is an ally of sorts. However, Villagiulio soon turns against Muginami for taking the Vox unit for herself, causing Madoka to become angry.

Madoka, wanting to take revenge against Villagiulio, stands against him in a battle. However, Muginami ends up activating her Vox unit and standing in Madoka's way, telling her that she's only being selfish in trying to take revenge on her behalf. As Madoka argues with her, a mysterious occurrence causes a mysterious flower known as Lagrange to rain from the sky.

As Madoka becomes conflicted about Muginami's actions, she comes to realise that she hasn't taken Muginami's feelings into account and decides to try and make up with her.

Asteria Lizamarie de Roschefall, the granddaughter of Novumundos' chairman, comes to question Madoka about the incident that occurred whilst confronting Muginami. As Asteria speaks with Yoko about the Voxs, Lan tells Madoka about the Vox Legend, in which an incident involving Voxes nearly destroyed the world 20,000 years ago. After speaking with Yoko, Asteria decides to ban Madoka from piloting Midori, prompting Lan and Muginami to lock themselves in the hangar as protest. However, Madoka decides to accept the ban, since it wouldn't separate her from Lan and Muginami. Afterwards, Asteria goes to see Villagiulo, refusing to hand over the Vox units.

As the Jersey Club works on a preparing a cultural festival, Izo becomes inspired by a samurai drama to challenge Madoka to a duel and travels to Kamogawa, prompting Array and Kirius to try and stop him. As Izo is mistaken by some of the other students for Madoka's boyfriend, he is told how Madoka was inspired by Yoko to join the Jersey Club after her mother died trying to save someone. After hearing the story, Izo decides to leave before Madoka arrives.

On the day of the cultural festival, Lan and Muginami have to keep a mission given to them a secret from Madoka. Whilst looking around the stalls they helped with, the girls come across Asteria who has Madoka escort her around the festival. As Madoka starts to become depressed at the thought of Lan and Muginami making new friends, she learns from Asteria about the assault Lan and Muginami are making and decides to go after them.

As Madoka approaches Pharos, Midori reacts to her presence and transmits her thoughts to Lan and Muginami, asking Tadoroko to try and get her ban lifted. As the two begin their attack against the enemy, the fleet focuses their attack on Lan whilst Muginami comes up against Villagiulo and a section of the fleet goes to attack Pharos. As Yoko reveals some of her research on the ancient people to Asteria, she manages to convince her to lift Madoka's ban, allowing her to fly up and assist her friends. As the enemy fires at Kamogawa, Kirius, Izo and Array stand to protect it. Just as the girls gain an advantage, Yoko gets critically injured when an enemy Ovid lands in the school, causing Madoka to become stressed which in turn causes the Voxes to once again go out of control and bloom Rinne flowers.

As reaction of the Voxes causes a large energy field to appear in the sky, Madoka subconsciously speaks with the ancient princess of La Garite, Yurikano, who tells her to follow her own path. Motivate, Madoka regains control of Midori and, along with Lan and Muginami, changes the energy field into a beautiful flower. As Madoka learns that Yoko is still alive, Midori suddenly shuts down and is targeted by Villagiulo. However, he is stopped by the arrival of the Le Garite army, prompting Muginami to leave with him in order to save him. Two weeks following the incident, Lan's identity as the Princess of Le Garite has since been revealed and she is due to return to her home planet. Going up to a 'Hill of Vows', Madoka and Lan make a promise that they, along with Muginami, will once again meet in Kamigawa before parting ways. As Autumn comes, Asteria reveals her insignia to Yoko whilst Madoka receives a letter from Muginami