As artificial intelligence (AI) becomes increasingly embedded in digital, social, and institutional infrastructures, and AI and platforms are merged into hybrid structures, systemic risk has emerged as a critical but undertheorized challenge. In this paper, we develop a rigorous framework for understanding systemic risk in AI, platform, and hybrid system governance, drawing on insights from finance, complex systems theory, climate change, and cybersecurity - domains where systemic risk has already shaped regulatory responses. We argue that recent legislation, including the EU's AI Act and Digital Services Act (DSA), invokes systemic risk but relies on narrow or ambiguous characterizations of this notion, sometimes reducing this risk to specific capabilities present in frontier AI models, or to harms occurring in economic market settings. The DSA, we show, actually does a better job at identifying systemic risk than the more recent AI Act. Our framework highlights novel risk pathways, including the possibility of systemic failures arising from the interaction of multiple AI agents. We identify four levels of AI-related systemic risk and emphasize that discrimination at scale and systematic hallucinations, despite their capacity to destabilize institutions and fundamental rights, may not fall under current legal definitions, given the AI Act's focus on frontier model capabilities. We then test the DSA, the AI Act, and our own framework on five key examples, and propose reforms that broaden systemic risk assessments, strengthen coordination between regulatory regimes, and explicitly incorporate collective harms.

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