This study aimed to address the mental health challenges faced by refugee artists who are grantees of ICORN—the International Cities of Refuge Network—from the perspective of the extended conceptual ADAPT model. The study employed exploratory qualitative research, and data were collected through semi-structured interviews with ICORN artists in Poland, Norway, and Sweden. For data analysis, Interpretive Phenomenological Analysis (IPA) was used, whereas for the presentation of the results, the framework of the ADAPT model was applied. The results showed that the super-ordinate themes that emerged from the IPA analysis related directly to the ADAPT model and could mostly be assigned to its basic pillars: (1) Security; (2) Bonds and Networks; (3) Justice; (4) Roles and Identities; and (5) Existential Meaning. However, the model was insufficient for capturing the full diversity of experiences described by the respondents. Therefore, an extension of the model in the form of two additional pillars, Art and Body and Mind, was proposed. The findings confirm that the ADAPT model is adequate for systematizing and depicting in detail the experiences of migrants/refugees. However, further modifications of the model are necessary, particularly the additional pillar Body and Mind, which has the potential to become a separate category in other migrants’/refugees’ assessment frameworks. Moreover, Art itself could be seen as a universal bridging factor between the refugee and the host population, contributing to the refugees’ adaptation to the host society.