Sword Art Online Progressive Scherzo of Deep Night, Vol. 2 (manga)

Kirito and Asuna have learned a dangerous secret: the fifth-floor boss will drop a powerful item that might overturn the fragile relationship between the two strongest guilds! On top of that, the intrepid pair stumble across a Romeo-and-Juliet-style story between the guilds that gives them some distracting ideas about how dating in the game could work. But all that will have to wait until after they assemble a team to defeat the boss and stop the brewing conflict!