Shinseiki Evangelion: Ikari Shinji Ikusei Keikaku

Dark Horse:
Stunning, hotheaded Asuka Langley Soryu has been friends with Shinji Ikari since they were little. And she always sort of assumed they'd stay together-until the day the beautiful, brilliant Rei Ayanami showed up in class! When Shinji starts to get curious about Rei, Asuka needs to figure out if she wants to be just friends with Shinji, or something more. But why are so many people keeping an eye on these relationships-people like homeroom teacher Misato, school nurse Ritsuko, and Shinji's mother-NERV's chief scientist, Yui Ikari...?
Ikusei Keikaku means something along the lines of "Raising Project", and is a series of games that are based around the concepts of Gainax's old Princess Maker games. These games allow you to more or less "raise" the character as if you were some sort of parental figure. Don't ask me for the particulars, I've never played it or seen it in action. But you can more or less mold the character into the adult you would like them to be. Previously there have been Rei and Asuka raising games, and most recently, a Shinji raising game. For some peculiar reason, they decided to release a manga to tie into the new raising game.
The manga begins in a manner quite similar to the alternate universe of episode 26 of the TV series, as well as the Girlfriend of Steel 2 manga. In that aspect, this manga will seem quite "familiar" to you.