Melonbooks just announced another new Party Box compilation for C91, with 2 new Butaotome songs! The titles are “Akuryou no Mita Akumu” (悪霊の見た悪夢) and “Tanoshii Sensou no Uta” (楽しい戦争のうた). Their original themes are unknown, and samples are currently not available.
Also, the third disc will contain old tracks from the circles participating, and Buta’s track is Daruma-san ga koronda (probably it will be unchanged from its original on Getsumen Tansa)
EDIT: Samples are up! The original themes for the new tracks are respectively Reincarnation and Great Fairy Wars ~ Fairy Wars. Also, surprisingly, Daruma-san ga koronda is a bit different, it has an additional 8-bit effect!