Just watched Possession with my girlfriend and enjoyed it. Fun movie, though it was a bit confusing towards the end there. My GF didn't seem to like it as much though.
Honestly, it reminds me a lot of a visual novel I read called Saya no Uta, though that made me a lot more uncomfortable and freaked out. Crank up Possession about 2 clicks on the fuck-up-O-Meter and add in a dash of Cthulhu and you get Saya no Uta.