As deep learning models become larger and more expensive, many practitioners turn to fine-tuning APIs. These web services allow fine-tuning a model between two parties: the client that provides the data, and the server that hosts the model. While convenient, these APIs raise a new concern: the data of the client is at risk of privacy breach during the training procedure. This challenge presents an important practical case of vertical federated learning, where the two parties perform parameter-efficient fine-tuning (PEFT) of a large model. In this study, we systematically search for a way to fine-tune models over an API while keeping the labels private. We analyze the privacy of LoRA, a popular approach for parameter-efficient fine-tuning when training over an API. Using this analysis, we propose P$^3$EFT, a multi-party split learning algorithm that takes advantage of existing PEFT properties to maintain privacy at a lower performance overhead. To validate our algorithm, we fine-tune DeBERTa-v2-XXLarge, Flan-T5 Large and LLaMA-2 7B using LoRA adapters on a range of NLP tasks. We find that P$^3$EFT is competitive with existing privacy-preserving methods in multi-party and two-party setups while having higher accuracy.