Kegan described the core transition between his stages as a subject-object distinction which feels like a take that emphasizes a self-oriented internal view. Another possibility is that the transition involves the machinery by which we do theory of mind. I.e. Kegan 5 is about having theory of mind about Kegan stage 4 such that you can reason about what other people are doing when they do Kegan 4 mental moves. If true, this might imply that internal family systems could help people level up by engaging their social cognition and ability to model a belief that 'someone else' has.
This would tie Kegan more closely/continuously with traditional childhood psychological development. Introspecting on my own experience, it feels like Theory of Mind is an underrated explanation for interpersonal differences in how people experience the world.