The widely accepted globalization of innovation entails two interrelated undertheorized aspects: (1) the capacity of certain firms to orchestrate transnational innovation systems appropriating successful results, which some have explained with the concept of corporate innovation systems (CIS), and (2) the co-existence of such globalization with those CIS and national innovation systems. I address these matters analysing US Big Tech artificial intelligence (AI) CIS showing that they combine multiple mechanisms to co-produce and appropriate AI. I propose ‘frenemy’ to describe Microsoft’s strategy because many Chinese organizations and even direct competitors integrate its CIS. ‘University’ symbolises Google’s strategy, given its focus on fundamental AI, its central place in the AI research field and appropriation mechanisms that are not translating into clear business advantages. ‘Secrecy’ defines Amazon’s strategy, maximizing knowledge inflows while minimizing outflows. Facebook, with the narrowest AI CIS, exhibits an ‘application-centred’ strategy. Ultimately, this paper contributes to understanding the multiple mechanisms used by leading corporations for controlling and shaping frontier transnational knowledge production and appropriation. By doing so, it advances our knowledge of the interplay between different innovation spheres (national, global and corporate) and highlights the dangers of CIS’s encroachment of national and global systems.