How do we design for intersubjective, digitally-mediated encounters in the museum? We report on the process of designing a digital interactive installation called Sit with Me for a permanent museum exhibition on migration in Newcastle upon Tyne, UK. Focussing on this case-study, the article aims to unpick the tensions, challenges and opportunities arising from designing for intersubjectivity in the context of migration exhibitions. It particularly explores how perspectives from the past may be brought into a relation with contemporary visitor perspectives through the design of interaction spaces that enable dialogicality and other-oriented perspective taking. Our aim is to enrich current museological discourse on exhibiting and experiencing migration in museums, contributing much needed understandings on the use and role of digital interactive technologies in these contexts; we further contribute methodological insight about a research-through-design practice that critically addressed the museum's desire to foster intersubjectivity in the encounters between Self and Other.