Yuuki and Yui becoming a couple will be the true canon ending.
There's a lot of build-up about the growing romance between Yuuki and Yui, probably planned by the creators. The series might end with Yuuki and Yui, both now older, at their adult years, walking down a open grassland with their child, a daughter.
Perhaps Yuuki will have a relationship with both Pecorine and Yui.
There'll be multiple alternate endings.
There will be non-canon but possible routes should Yuuki chooses another girl.
Pecorine: The two will rule over the kingdom belonging to Pecorine's family, with Pecorine as Queen and Yuuki her Royal Consort/King. In typical Pecorine fashion, their route will end with everybody they know, sitting together in a big hall enjoying a lovely feast together.
Kokkoro: It fast-forwards to several years later when Yuuki and Kokkoro get married.
Karyl: Yuuki will clean up Kary's room much to her embarrassment and secret happiness.
Rei: Rei will forsake her rights to claim the family fortune and live as a commoner with Yuuki.
Hiyori: Hiyori and Yuuki set off to do some good.
Saren: Yuuki, who is now Saren's husband will be working as her secretary.
Suzume: Following his marriage to Suzume, Yuuki will become Saren's butler. When Suzume fails at yet another simple task, she drops to her knees and sighs dejectedly. A moment later a hand will appear in front of her. She looks up to find Yuuki at her side with his typical smile on his face, one hand outstretched, the other giving her a thumbs up. Smiling to herself, Suzume takes his hand, stands up again and vows to do better.
Ayame:
Kurumi:
Maho: Settles down with Yuuki, her new husband, to open a toy and book shop. At the end of their route, Maho moves towards a big chair in a corner of the shop that is surrounded by plushies. She sits down, holding a book. Opening the book, she begins to tell a group of children (including a couple of her own) that this is a story she has written herself. It is a tale about a Princess and her Princely Knight.
Makoto: Either Yui lets Makoto have Yuuki or Makoto and Yui decide to engage in a threesome with Yuuki.
Kasumi: Kasumi becomes a real detective and Yuuki follows her as his assistant.
Kaori:
Misato: Despite the age difference, Misato and Yuuki marry. They then open a nursery of their own. The route ends with Misato giving Yuuki and their child a lap pillow.
Aoi: Yuuki and Aoi, now a couple, go to a social. Aoi clutches Yuuki's arm nervously, but when he gives her a reassuring smile and thumbs up, she stops being nervous and introduces herself to someone.
Hatsune: The route ends with an epilogue several years having passed where Hatsune and Yuuki have married and have a child together. The two are getting their baby to sleep but not before having to deal with some superpower antics the baby inherited from their mother.
Mahiru: Mahiru officially opens the biggest farm in Japan ending with some puns which only Yuuki laughs at while the others just confused and dismayed.
Shiori: Ends with the both of them exiting the hospital with Shiori now full healthy.
Lima: Lima and Yuuki will be at the outback with Lima giving Yuuki a ride.
Rin:
Ruka: Yuuki becomes Ruka's right-hand man and the two lead the gangs against anyone who disturb the peace.
Eriko: She and Yuuki start a relationship and just go on a normal date....that's it.
Mitsuki: After finally getting married, Mitsuki asks Yuuki to let the two of them have their honey moon now to....you know.
Nanaka: Nanaka and Yuuki will start a series of fanfilms before it gets attentions and they direct their own television series.
Anna: She and Yuuki become full-time bounty hunters and travel the world to stop bad guys and protect the innocent.
Labyrista:
Shizuru: Shizuru and Yuuki do become a couple but Shizuru has to go to college. Howwever, the two still keep in contact with each other.
Rino:
Akino: Akino and Yuuki get married and later dine in a burger joint, while still wearing their wedding attire. Yuuki sighs but still smiles, knowing Akino's education will continue.
Yukari: Yukari and Yuuki will have a relationship despite the age gap between them. The route ends with the two attending the party leading Yukari vomiting on her boyfriend.
Mifuyu: The route ends with Mifuyu using her saved earnings to go on vacation with Yuuki.
Tamaki: Tamaki and Yuuki find a stray kitten and adopt them.
Mimi: Will give Yuuki a "Big-Sis" hug.
Misogi: Misogi becomes an adventuring archaeologist and travels the world to find treasure and adventure. Yuuki comes along to keep her company.
Kyouka: Kyouka reach her teens, allowing her to be eligible to date Yuuki. Unfortunately, Yuuki has to go overseas to college but he and Kyouka will still keep in contact.
Nozomi: Nozomi does a private singing performance for Yuuki.
Tsumugi: Tsumugi either does a threesome with Yuuki and Rei or let's go of Rei and be with Yuuki.
Chika: Both Yuuki and Chika becomes a music duo.
Ilya: Ilya turns Yuuki into a vampire and the two remained together many, MANY years later.
Shinobu: Shinobu and Yuuki become a couple and the former's father parts to the afterlife after giving his blessings to Yuuki.
Yori:
Akari:
Miyako: She and Yuuki open a sweet and PUDDING store.
Jun: Jun and Yuuki will work a series of short films centering on a heroic black knight.
Christina:
Tomo: They continue to date after waking up and eventually marry when Tomo graduates high school and inherits her family’s dojo.
Matsuri:
Suzuna: Suzuna finally finishes school but learns that she now has to face college. Despite knowing the future hardships, she doesn't mind because she has Yuuki by her side.
Io: After finally graduating from school and finishing college, Yuuki marries Io despite their significant age gap.
Misaki:
Yuuki is not the one guy all of the girls fell in love with.
The memories of their supposed life experiences with him irl are in fact implanted into the girls and Yuuki by a third party, possibly Ameth. The only one whose memories of this time are genuine will be the player’s choice.
To everyone else, Yuuki is merely being used as a stand-in for another guy that they had these relationships with.
