The extras don't add anything to the story. (None of the extras in the other games did either, it's all optional after all.)

the extra stuff is to complete getting BTs (You'd need to play through the game many times for that anyway.), beating the optional dungeon, bosses, and seeing Lenneth and Freya in cute chibi-form. ( ) And leveling up. Alot. And getting powerful weapons and stuff. Y'know, like any other bonus dungeon in any other tri-Ace game, and RPGs in general.