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.

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.