First, the characters:
Haruno (Ignis) - Cover Heroine of Concerto 1
Touka (Luna) - Cover Heroine of Concerto 2
Shuntarou - Childhood friend of Haruno
Mifuyu - Touka's younger sister
Ichika - Scientist, part of an organisation
Kamishin/Doctor - Scientist, in the same organisation as Ichika
There are 'gilt seeds' (I will just call it seed) being spread across the streets; These seeds has the qualities to amplify people's carnal desires, and will eventually turn people into monsters if the desires exceed the limits. The seeds came from an alternate world as part of a plan to invade the world but the invader defeated by Exstia (I do not know if it is the heroines from main Exstia series) years ago, and were kept by the organisation until the seeds were stolen by an unknown individual/group and somehow ended up on the streets.
[Events which occur during Concerto 1] As Haruno and Shuntarou were getting attacked by a monster, Ichika gave Haruno a device which allowed her to transform into an Exstia (Ignis). Ichika asks Haruno for her help in retrieving the seeds.
Similarly, in a separate occasion as Touka and Mifuyu were getting attacked, Doctor gave Touka a device which also allowed her to transform into an Exstia (Luna). Doctor brings them to his laboratory and informs Touka that Mifuyu have signs of the seed in her body and he will require the seeds in order to treat Mifuyu.
Afterwards, the story goes into -> Monster appears, Ignis defeats it, repeat. Last boss is a merged monster which Ignis and Luna team up to defeat.
In corruption route, Doctor is responsible for infusing seed onto Haruno which eventually turns her into Dark Exstia.
In the entirety of Concerto 1, both heroines do not know the true identity of each other, and although they will meet each other at times, they work separately.
[Events which occur during Concerto 2] After the introductions, story continues from Concerto 1. Touka is starting to feel anxious over the fact that most of the seeds are being collected by Ignis which are needed for Mifuyu's treatment. Again, story goes -> Monster appears, Luna defeats it, repeat. This time however, Ignis also will arrive to location where the monsters were detected and retrieves the seed which causes Touka to be more worked up. Ignis and Luna will battle with each other over possession of the seed a couple of times, which ends with Ignis winning in all of them. Under Doctor's suggestion, he injects a serum into Touka to increase her combat capabilities (Touka does not know that the serum is actually made of materials from the seed).
Ignis and Luna battles with each other one last time, and this is where it splits between good route and corruption route. In both routes Haruno and Touka learns of each other's true identity. In corruption route, the Doctor creates monsters and Luna loses, and turns into Dark Exstia. Ignis also turns into Dark Exstia here.
In good route, Haruno and Touka (as well as others) confront Doctor at his laboratory. Doctor turns himself into a monster but loses to the Exstia duo. With the essence of the seed (due to the serum) still in Touka, she suddenly starts to feel pain and Ichika believes she is being turned into a monster. Mifuyu then hugs Touka which causes the essence to be transferred to her, and she suddenly turns into an Exstia with the power of the seed. While she is not considered a Dark Exstia and still loves her older sister, she has a warped sense of morality; Luna stops her and restores her back to normal. Game ends with Touka cheerfully greeting Haruno at school.
For Doctor, he is obssessed with creating the perfect Human Organism hence his actions in Concerto 1 and 2.
I have omitted some stuff, so anyone interested to know about the story in detail should try the game out!