Released for the PSP in 2013,
Corpse Party: Book of Shadows serves as an encyclopaedia of insight into the world and lore of the previous game. Continuing the story from wrong ends, as well as contributing tales from before, during, and after the first game, it serves to develop characters and throw interesting "what if" scenarios at you.
Be aware the review below contains minor spoilers for the events of the first game, this largely unavoidable given how closely related it is to
Book of Shadows. If you are interested in this, I urge you to look at
Corpse Party first.
Official Review