In cocreating value with other organizations, nonprofit organizations may face multiple management challenges, posed by multistakeholder global innovation networks. Since these have not yet been systematically studied by academics, this study explores how nonprofit organizations can promote the cocreation of value in multistakeholder global innovation networks. Adopting a longitudinal single-case study approach from the perspective of network orchestration theory, this work deeply analyzes how nonprofit organizations can promote the evolution of the global innovation network of the COVID-19 vaccine under the COVAX program. The results show that nonprofits need to successively address the dilemmas of legitimacy, direction, and heterogeneity in constructing global innovation networks and that to solve these stage dilemmas, orchestrators must successively function as network architects, liaisons, and leaders to direct the implementation of network actions using trusted, leveraged, and adapted orchestration logics. This paper further proposes a model of the orchestration process and mechanisms by which nonprofit organizations facilitate multistakeholder global innovation networks. Theoretically, this study therefore extends network orchestration theory by summarizing the mechanisms and orchestration logics by which NPOs construct and develop networks when they act as orchestrators. From a practical perspective, this study also provides guidance for future unexpected global public health crises, improving the global community's ability to combat them.