How can personal identity be determined in such a way that developments, experiences and other dynamic and context-dependent aspects of that identity can be taken into account? For several decades now, the narrative, the story, has often been referred to in answering this question as a cognitive instrument that can adequately deal with those aspects. The monologue thus appears to present itself as a medium in which personal or autobiographical identity is formed. However, what happens when we place the identity narrative in a dialogue: when two people with very diverse backgrounds have a dialogue that touches on their identity? Does this perhaps provide an entirely new challenge and enrichment of that narrative, which can have a major impact on both the individual and the relationship? I want to explore these questions in this article, motivated by both the philosophical perspective and my experiences as co-initiator of the "Keti Koti Table", in which such a dialogue plays a central role. To this end, I will first discuss the dynamic aspects of the narrative, in which the phenomenon of "refiguration" as presented by Ricoeur is key. This is then discussed in the context of the dialogue. In § 4 I discuss the specific dialogue method that we have developed for the Keti Koti Table. Subsequently, in § 5, some experiences of participants are discussed, whose identity refigurations are analyzed under the influence of the dialogue in § 6. It is concluded with a brief conclusion about the special significance of the dialogue for the narrative self-constitution in a diverse society.