To cope effectively with the impacts of climate change, people will need to change existing practices or behaviours within existing social–ecological systems (adaptation) or enact more fundamental changes that can alter dominant social–ecological relationships and create new systems or futures (transformation). Here we use multilevel network modelling to examine how different domains of adaptive capacity—assets, flexibility, organization, learning, socio-cognitive constructs and agency—are related to adaptive and transformative actions. We find evidence consistent with an influence process in which aspects of social organization (exposure to others in social networks) encourage both adaptive and transformative actions among Papua New Guinean islanders experiencing climate change impacts. Adaptive and transformative actions are also related to social–ecological network structures between people and ecological resources that enable learning and the internalization of ecological feedbacks. Agency is also key, yet we show that while perceived power may encourage adaptations, it may discourage more transformative actions.