This paper presents a multilevel, multistage approach to system of systems engineering optimization where a system design/selection is linked with system allocation along the multistage decision making horizon. The approach is composed of two parts: pseudo-hierarchical formulation (i.e., how to model the stages of multiple, separate decision making processes), and multistage coordination (i.e., how efficiently the proposed model would perform). The pseudo-hierarchical formulation expands the analytical target cascading previously developed by the author into multiple stages to capture level-by-level and stage-by-stage system of systems design optimization. The multistage coordination is based on the alternating directions method that is incorporated as an efficient means to solve this inherently large-scale optimization problem. An airline example validates the methodology where an airline plans to introduce multiple new aircraft to capture dynamically changing future demand of the customers. The proposed methodology is validated against the all-in-one approach and the sequential approach.