On re-examining my reply, I realize I left open the parallel question to the mind-body problem of what is the relationship between the physical and spiritual – and this connects directly to the issues addressed in the title and OP of the thread regarding an immaterial “soul.” Substance monism of course doesn’t suffer from the same logical problems as dualism, but I still haven’t addressed the question directly. My answer to this connects to the more general question of relationships between spiritual things. If spiritual things are what they are by their own nature alone then there is no system of relationships to put one thing into relationship with another. The result is that all relationships have to come from within themselves as a product of their own nature.
This general principle can be applied to the relationship between spiritual and physical. The nature of the physical is the mathematical space-time relationships which severely limits the ways in which anything spiritual can affect it. My hypothesis is that the human spirit, however, derives its nature from choices made by a living human being. I believe this explains a great deal of the claims made in religion. It also means that the relationship between the physical and spiritual is largely but not completely an epi-phenomenal one – i.e. mostly a matter of the physical influencing the spiritual and only a very small window through which the spiritual can influence the physical (which I propose isn’t too much of an obstacle to a omnipotent omniscient God, so there is no support for Deism in this).