So let's say someone stored a bit of their soul in another person, deliberately. Could that bit of soul take over the person and possess them?
We know Harry was an unintentional Horcrux with a bit of Voldemort's soul, but that it did not ever take over Harry. Neither Harry nor Voldemort were aware of that piece of soul. There was a connection between Harry and the powers that Voldemort had, and once Voldemort returned there was an even stronger connection into Voldemort's mind. Yet Voldemort did not know about piece of soul in Harry, even after he tried to possess him in OotP and failed.
But what if someone hid their soul in another person on purpose? What if that piece of soul was more aware? Could it take over the person, especially if the person let it? We know Ginny's diary possessed her at times, so it seems possible to me. Then there is the locket as well, which obviously influenced the people who wore it.
Really, I think anything is possible with magic, so what's necessary to make it believable as a reader? What am I not considering when it comes to possession?