Buddha set a good example on this topic, by beginning any discussion like this by asking exactly what is meant by soul. This is no small matter, not easily determined, and views tend to be influenced by not only religious traditions but many social and cultural factors eg. literature.
I like Aristotle's views On The Soul. He proposed a kind of 'multiple soul', based on his carefully derived definition, with something like: biological nature, supervened over by nervous system, supervened by conscious nature. He saw these souls as located in our whole bodies and conditioned by them, even though he thought the conscious nature could survive without the body.
What might survive the body is not an easy question for people that believe this. In the West afterlife ideas are generally shaped by revelation from holy people, although heaven and hell were not clearly articulated in scripture (the Myth of Er recounted by Plato is a counter-example, a near-death experience) . In India ideas about rebirth are generally shaped by holy people who claim direct knowledge and recall of past lives. This faces two main problems: what survives transmigration in someone with no memory of past lives, and given that memory is a key aspect of personality how much is someone the same peson as the person in a past life? It seems some level of abstraction is at work, the later self inheriting how use of the conscious mind had conditioned, rather than memories in nearly all cases.
In the Yogacara school of Mahayana Buddhism, they extend the wider Buddhist model of six consciousnesses associated with five senses and the mind, to a total of eight consciousnesses. In this view, mind is more 'fundamental' than matter, and the persistence of things to different senses is a mental, karmic, process. The most abstract eighth consciousness of people is what transmigrates and is reborn, because it exists in a layer of phenomenal organisation called'storehouse consciousness'. A way of interpreting that might be, that at the more abstract level we become increasingly like archetypes, representative personality types, who encounter and respond to similar events in similar ways, and will get caught by similar karmic traps, until countervailing patterns and templates and resolutions liberate them. Buddhism though consistently challenges the idea of any persistent essence, and instead pictures causally linked chains of phenomena, like lighting one candle from another.
Treating the soul as a litle homunculus sat inside us is a category error. I suggest we need to think of different layers of organisation and abstraction, to find anything that can meaningfully be called a soul.