The first thing that has to be said is that the movie 'Jonathan' is fiction. There is no indication that the story is intended to be based on anything resembling real life. Christian theology does not deal with fictional situations, and so it is not really useful to ask what the Christian theological approach to an unreal situation is.
Multiple Personality Disorder does exist in real life, but looks very little like the movie. Where it occurs it is not seen as 'multiple people inhabiting a single body' by anyone, either medical professionals or Christian theologians. Instead it is seen as a single person exhibiting differing personality traits, and it is a disorder of the (one) mind that inhabits a body, and can be treated. There is no question of them having 'two souls'.
What is possible in Christian theology is that of a second spirit entering and sometimes taking over the body of a person - called 'possession'. Note that I carefully say 'possible' because most Christians would consider it a largely theoretical possibility, occurring only extremely rarely if at all, and that ancient (or modern) descriptions of possession were almost invariably instances of multiple personality disorder.
If we accept possession we must note that again there is no question of multiple souls for a single person. The possessing spirit is a separate entity from the person whose body it is, and can be cast out. The person has a single soul