The paper explores the challenges and opportunities of participatory approaches in the context of foundation models, which are large-scale AI systems capable of adapting to various tasks. While these models offer significant potential, they also pose risks of reinforcing existing power imbalances and causing disproportionate harm to marginalized groups. The paper argues that current participatory methods in AI/ML are not well-suited for foundation models due to their scale and domain-agnostic nature. To address this, the authors propose a three-layer framework for participatory foundation models: the foundation layer, subfloor layer, and surface layer. The foundation layer is where the base model is created, the subfloor layer provides technical infrastructure and governance for a specific domain, and the surface layer allows affected communities to shape the use of the model for specific tasks. The framework aims to create more meaningful opportunities for participation by allowing local, application-oriented engagement while avoiding duplication of effort. The paper presents three case studies in clinical care, financial services, and journalism to illustrate how this multi-layer model can support public power and decision-making over ML in the foundation model paradigm. The authors conclude that participatory approaches can help mitigate the risks of foundation models by ensuring that diverse stakeholders have a voice in their development and use.The paper explores the challenges and opportunities of participatory approaches in the context of foundation models, which are large-scale AI systems capable of adapting to various tasks. While these models offer significant potential, they also pose risks of reinforcing existing power imbalances and causing disproportionate harm to marginalized groups. The paper argues that current participatory methods in AI/ML are not well-suited for foundation models due to their scale and domain-agnostic nature. To address this, the authors propose a three-layer framework for participatory foundation models: the foundation layer, subfloor layer, and surface layer. The foundation layer is where the base model is created, the subfloor layer provides technical infrastructure and governance for a specific domain, and the surface layer allows affected communities to shape the use of the model for specific tasks. The framework aims to create more meaningful opportunities for participation by allowing local, application-oriented engagement while avoiding duplication of effort. The paper presents three case studies in clinical care, financial services, and journalism to illustrate how this multi-layer model can support public power and decision-making over ML in the foundation model paradigm. The authors conclude that participatory approaches can help mitigate the risks of foundation models by ensuring that diverse stakeholders have a voice in their development and use.