Yes, you just need to click new save as many times as you need. There shouldn't be any problems with this.
Everytime I save it, it just overrides the current save file. For example I want to have 2 save files where one is for going the Hitomi route and the other file is the Yuki route.
Try to delete all the saves, and then save again. Maybe that's the problem?
Its working now. Thanks!