An optimization-based multilayer operability framework is introduced for the process design of nonlinear energy systems that are challenged by complexity and highly constrained environments. In the first layer of this framework, a mixed-integer linear programming (MILP)-based iterative algorithm considers the minimization of the footprint and the achievement of process intensification targets. Then, in the second layer, an operability analysis is performed to incorporate into the approach key features for optimality and feasibility, accounting for the system operation with changeable input conditions. The outcome of the framework consists of a set of modular designs, considering the aspects of both size and process operability. For this study, the nonlinear system is represented by multiple linearized models, resulting in low computational expense and efficient quantification of operability regions. The developed framework is applied to a membrane reactor for direct methane aromatization conversion to hydrogen and benzene. Subsystems of dimensionalities of 2 x 2 and 3 x 3 (design inputs x outputs) are considered in the first layer to obtain a modular design region. The possible modular designs inside this region are then ranked according to an operability index obtained from an additional 3 x 3 (operational inputs x outputs) mapping. This step analyzes the effect of operational inputs, producing a mapping of total dimensionality of 6 x 3 (inputs x outputs). The application of the developed framework generates two candidate designs for system modularity, the most operable design and the optimal design with respect to process intensification in terms of footprint minimization. The developed framework thus provides guidelines for obtaining modular designs that simultaneously consider process intensification and operability aspects.