There have been rumours of a new Parasite Eve game for PS4. Plus the fact that 3rd Birthday (PSP) reached its sales target (0.5M), it doesn't seem like an unlikely scenario.
3rd's gameplay was mostly good, I'm fine with keeping that while adding something to make it slightly less repetitive. The RPG elements should definitely stay, particularly the DNA system.
They do need to bring back snarky Aya instead of whimpering Aya though... that's the main thing they gotta avoid from the PSP game.
As for who's making it, well HexaDrive made 3rd... Right now they're collaborating with SE in FFXV and they finished the Type-0 port but I think that leaves enough room for them to be the developers. Seeing as how pretty much everything (that OST!!) except characterization was good in the PSP game, they just need to get a different writer and then it'll be in good hands.
