For workloads that place strenuous demands on system software, novel operating system designs like unikernels, library OSes, and hybrid runtimes offer a promising path forward. However, while these systems can outperform general-purpose OSes, they have limited ability to support legacy applications. Multi-OS environments, where the application’s execution is split between a compute plane and a data plane operating system, can address this challenge, but reasoning about the performance of applications that run in such a split execution environment is currently guided only by expert intuition and empirical analysis. As the level of specialization in system software and hardware continues to increase, there is both a pressing need and ripe opportunity for investigating analytical models that can predict application performance and guide programmers’ intuition when considering multi-OS environments. In this paper we present such a model to place bounds on application speedup, beginning with a simple, intuitive formulation, and progressing to a more refined, predictive model. We present an analysis of the model, apply it to a diverse set of benchmarks, and evaluate it using a prototype measurement tool for analyzing workload characteristics relevant for multi-OS environments.