The fourth industrial revolution challenges the existing understanding of innovation and upgrading in the global economy. It blurs traditional sectoral boundaries based on distinctive products and technologies and calls into question a traditional global value chain (GVC) perspective, which, similar to the sectoral systems of innovation approach, examines innovation and upgrading from a sector-based orientation. Building upon the recent reformulation and extension of GVC governance theory, this article proposes the notion of cross-sectoral GVC governance to capture the new stage of platform-based industrial development. It specifies the conceptual dimensions of cross-sectoral GVC governance in terms of the mode of governance (i.e., driving, linking, and normalizing), the overall GVC structure in terms of polarity, and firm strategies of managing GVCs. The proposed framework is illustrated using the case of smartphones as a platform product, focusing on four lead firms - Samsung, Apple, Huawei, and Google - to showcase divergent firm strategies for governing cross-sectoral linkages related to innovation and upgrading.