Abstract Living together in culturally plural societies poses numerous challenges for members of ethnocultural groups and for the larger society. An important goal of these societies is to achieve positive intercultural relations among all their peoples. Successful management of these relations depends on many factors including a research‐based understanding of the historical, political, economic, religious and psychological features of the groups that are in contact. The core question is ‘how we shall we all live together?’ In the project reported in this paper (Mutual Intercultural Relations in Plural Societies; MIRIPS), we seek to provide such research by reviewing three core psychological hypotheses of intercultural relations (multiculturalism, contact and integration) in 21 culturally plural societies. The main goal of the project is to evaluate these hypotheses across societies within the MIRIPS project in order to identify if there are some basic psychological principles that underlie intercultural relations panculturally. If there are, the eventual goal is to employ the findings to propose some policies and programmes that may improve the quality of intercultural relationship globally. An internal meta‐analysis using the MIRIPS project data showed that the empirical findings from these societies generally support the validity of the three hypotheses. Implications for the development of policies and programmes to enhance the quality of intercultural relations are discussed.