Growing evidence supports the importance of culturally appropriate mental health interventions, yet it is not always feasible to develop culturally grounded interventions or adapt existing interventions for each cultural group. In addition, these approaches do not recognize the multiple intersecting aspects of culture and identity that individuals, families, and communities possess. Thus, an essential question is whether culturally appropriate mental health interventions have to be culturally specific. We address this question by examining processes of the Refugee Well‐being Project (RWP), a community‐based mental health intervention for refugees resettled in the United States, which included people from multiple cultural groups (Afghanistan, Great Lakes region of Africa, Iraq, and Syria) and was grounded in common experiences of forcibly displaced people from marginalized backgrounds. RWP incorporates a practice‐based concept of culture, an intersectional view of identity, and a multilevel approach to address postmigration stressors. Semistructured qualitative interviews were conducted with 290 participants at preintervention, followed by interviews at three timepoints with a purposively selected subsample (n = 66). Additional interviews (n = 101) were conducted with refugee and student partners. Four themes demonstrated key principles for creating culturally appropriate interventions with diverse groups: (a) recognize cultural complexity in practice; (b) focus on how racism and discrimination are experienced in everyday life; (c) de‐center dominant US culture; and (d) create an egalitarian, inclusive space to put principles into action. We conclude that mental health interventions implemented with multiple, diverse groups can be culturally appropriate and effective without being culturally specific.