Assuming for the sake of argument that there is such a thing as multiple personality disorder, where a single human body manifests several distinct, consistent and lucid personalities are manifest at different times.
Do each of these personalities (to all intents and purposes different people, save for physically) posess a separate soul?
Well, first you have to define ‘soul’, and accept that there is such a thing in the first place. Since it’s impossible to prove the existence of a ‘soul’, let alone isolate a particular concept of a ‘soul’, you’re probably going to find yourself stuck pretty quickly.
Why stop there?
If I suffer brain damage and develop a distinct personality and complete loss of previous memory as a result do I still have the same soul? If not then what happens to the old soul? Is it in heaven, limbo, purgatory? If I do keep the same soul then where’s the justice? The new persoanlity is a genuine saint but has to pay for the sins of the old. What if I’m a saint now and the new personality is a axe wielding homicidal manaic? Does my current soul pay for the sins of a personality I didn’t create, have do control over and that doesn’t even exist yet?
I’m not attempting a hijack here, just pointing out that there are other situations, a lot less debatable than multiple personality disorder, where one body is inhabited by two distinct personalities in sequence.
For my money there is only one soul in these circumstances. Now what’s the next question? (I know there’s going to be one.) 
I find it much easier to believe in MPD than the concept of a soul. Even if you assume we have one (or N), at what point in history/pre-history did we start getting them? Was there a generation of homo sapiens (or earlier species) where the parents didn’t have one, and the offspring did? If not, how could it be a gradual process?
We tried to discuss the issue of when humans/animals started having souls here, but it all went a bit wrong, sadly
Sorry, perhaps I should have stated that I was also assuming, for the sake of the discussion, that there is such a thing as a soul.
Good points.
Why do we drive on the Parkway and park on the driveway?
Oh my. Having just read the thread I think ‘a bit wrong’ is an understatement. That said, I did like this:
Ok, onwards and upwards. We’re assuming souls and MPD exist.
I’m not convinced by the 1-1 link between souls and personality (i.e. that if you increase one, you automatically have to increase the other). Insofar as personality is a function of upbringing, innate stuff, brain chemistry, whatever, these are pretty everyday, secular things. A soul surely should have some supernatural (not in the occult sense, but in the sense of somehow transcending nature) element?
This is probably tangential, but what would have been the point of casting out demons? If we posit > 1 souls, the usurped one is still on the way to heaven, the evil one on his way to somewhere considerably hotter presumably.
You know? I have absolutely no idea. If I had a drive (sans ‘way’) I’d park there, sure, but I’m pretty sure I don’t know what a Parkway is, or where to find one in the UK.
Perhaps Parkways are less universal than souls.
Interesting question, which, as previously noted, plays into the “moral culpability combined with brain injury” mode of questioning.
First cut answer: I don’t have a clue. Best source of answers to this sort of question is found by going into secret and asking your Father who is in secret… 
Second cut answer: On the presumption that material with explication in ancient sources of demon possession, etc., is equivalent to present-day mental illness, one finds Jesus casting out multiple demons from one woman, who was restored to “wholeness” (Luke’s term) by Him. Presumption is that she is thereafter one mentally and physically healthy individual, possessed of the requisite standard-issue one soul. Hence the demons who called themselves “Legion, for we are many” might be construed as multiple personalities and Jesus’s healing work as personality reintegration.
Generally, I never drive on the Parkay; it tends to make my tires sticky and put me in skids. Although it was cute to hear it go “butter!” in a high-pitched scream when I did drive over it.
My first Great Debate post!
According to many of the Eastern religions, and interpretations of these religions, personality and soul are two separate things. The personality is the “active” parts of the soul in this lifetime, that allow for the growth and healing of the larger soul over many lifetimes. So, IMHO, is would then seem that multiple personalities can still come be connected to the same soul. The individual personalities would each contain parts of the larger soul.