The Variable Cycle Engine (VCE) is considered a promising candidate for future advanced aircraft due to its significant performance advantages. However, its development is hindered by high research and development costs. The concept of derivative engines based on a common core offers an opportunity to utilize mature technologies, thereby reducing both costs and risks. Nonetheless, in derivative engines, cooling air, turbine inlet temperature, and cooling requirements are interdependent, rendering the derivative design challenging. This paper investigates the impact of cooling air on the engine matching mechanism and presents a performance model for the derivative VCE that incorporates cooling requirements. The model comprehensively evaluates the effects of cooling-air extraction and operating point variations on the derivative VCE’s performance. The findings reveal that cooling-air requirements can be translated into a boundary condition on the compressor characteristics. The feasible range for the operating point of the derivative engine is defined as the area below this boundary, where the cooling requirements can be met. By considering the influence of cooling requirements on operating point selection in the early design stages, this approach prevents issues related to unmet cooling requirements due to improper operating point. Furthermore, it provides valuable guidance for the optimization of derivative engine performance in subsequent stages.