Institutional logics are an important conceptual tool when designing and navigating public sector change. Our systematic review discovers how institutional logics clash or combine during healthcare change efforts. We identify logics that are more, or less compatible with each other and offer a framework that map logic relationships. We offer a typology of relationships between institutional logics: independent (constellations, loose coupling), interdependent (rebalancing, hybridization) and co-dependent (dominance, co-optation). We go beyond previous conceptions of logic relationships to characterize these relationship types, identify associated risks, and suggest that successful logic relationships includes clear boundaries, reciprocity, and a balance of power and control.