The emergence of foundation models, including language and vision models, has reshaped AI's landscape, offering capabilities across various applications. Deploying and fine-tuning these large models, like GPT-3 and BERT, presents challenges, especially in the current foundation model era. We introduce Emulator-Assisted Tuning (EAT) combined with Parameter-Efficient Fine-Tuning (PEFT) to form Parameter-Efficient Emulator-Assisted Tuning (PEAT). Further, we expand this into federated learning as Federated PEAT (FedPEAT). FedPEAT uses adapters, emulators, and PEFT for federated model tuning, enhancing model privacy and memory efficiency. Adapters adjust pre-trained models, while emulators give a compact representation of original models, addressing both privacy and efficiency. Adaptable to various neural networks, our approach also uses deep reinforcement learning for hyper-parameter optimization. We tested FedPEAT in a unique scenario with a server participating in collaborative federated tuning, showcasing its potential in tackling foundation model challenges.