As the field of management studies widens its scale of reflection to consider the socio-ecological ecosystems of which organizations are part, more attention is devoted to grand challenges. While extent literature generally treats them as exogenous objects, our focus here is on unfolding encounters with grand challenges. We conceive grand challenges as concrete problems of arbitration of more-than-human ways of life, where the managerial practices of organizations enact and transform grand challenges. We put forward a posthumanism and pragmatist style of thinking, which, we argue, can help us think with grand challenges and engage in creative ways of composing a common world. Through the story of a problematic situation where tangles of grand challenges abound, we offer a mode of construction that can help us compose what is, in a given situation, a ‘better’ world. This mode of construction is based on three sets of practices, namely, slowing down, multispecies world-making, and being present and grieving losses. It facilitates the emergence of new ways of composing the world, helps account for the implication of other species, and foregrounds the elaboration of worlds in a response-able way. Our paper contributes to the grand challenges literature by proposing a mode of attention and action that engages both management researchers and practitioners in the work of constructing multispecies worlds.