Frontier AI governance often centres on the model-level governance paradigm, which assumes that a model's capability profile is primarily a function of the compute and data used during training. This position paper argues that model-level governance becomes less effective when capability progress is increasingly driven by "non-model gains"--improvements that are independent from advances in the base model. We formalise the concept of non-model gains and provide a taxonomy of three distinct vectors of capability gain: inference gain (scaling compute at test-time), systems gain (post-training enhancements such as scaffolds), and asset gain (enhancing a model with restricted assets). We demonstrate how these vectors--alongside potential future impacts from embodiment, continual learning, and AI diffusion--may undermine risk management strategies that hinge mostly on pre-deployment evaluation and mitigation. We provide an overview of governance approaches that go beyond the model level: system, entity, agent, and cloud governance. Finally, we emphasise the importance of societal resilience as a complement to these governance layers.