ABSTRACT Social identity theory argues that conflict between groups diminishes if they discover they have something important in common, and if they can build a new hybrid identity together. With this premise in mind, the article demonstrates how present-day experiences of refugees, displaced ethnic groups, political exiles, foreign-born workers, diasporic populations and other migrants may be incorporated into the existing body of predominantly national historical landscapes and stories addressing expulsions, exile and forced displacement experienced by European populations in the twentieth century. It is argued that we should look closer at the compositional processes and orchestration of migrant heritage in Europe as an inherently political concept that may both amplify and interfere with social cohesion. The article discusses the compositional strategies (grafting, bifurcation and suture) that loosen up the structure of representations and have been used experimentally by four cultural institutions in Italy, Spain, Germany and Poland. The article maintains that series of hands-on small- and middle-scale experiments and compositional adjustments may be highly instrumental in enhancing the value of the heritage of forced migrations, not only as a domain of conflicting academic interpretations, but also as a factor of intercultural cohesion in a broader perspective.