Increasing thermal loads in air vehicles has recently driven a need for more efficient cooling mechanisms and novel control techniques. As such, multi-compressor vapor compression systems are being considered for next generation aircraft to help mitigate the effects of large magnitude and highly transient thermal loads. The inclusion of these systems coupled with the transient environment in which they operate leads to the need for advanced control techniques to select operational modes and handle continuous actuation. This work develops a switched linear model framework that is used in a hybrid model predictive controller to determine the operational mode of the system, and continuous actuator set points. While this approach is applicable to a wide range of systems, a sample aircraft simulation study shows the advantage of the predictive controller over current logic-based control strategies.