The paper addresses aggregation issues for composite (modular) solutions. A systemic view point is suggested for various aggregation problems. Several solution structures are considered: sets, set morphologies, trees, etc. Mainly, the aggregation approach is targeted to set morphologies. The aggregation problems are based on basic structures as substructure, superstructure, median/consensus, and extended median/consensus. In the last case, preliminary structure is built (e.g., substructure, median/consensus) and addition of solution elements is considered while taking into account profit of the additional elements and total resource constraint. Four aggregation strategies are examined: (i) extension strategy (designing a substructure of initial solutions as "system kernel" and extension of the substructure by additional elements); (ii) compression strategy (designing a superstructure of initial solutions and deletion of some its elements); (iii) combined strategy; and (iv) new design strategy to build a new solution over an extended domain of solution elements. Numerical real-world examples (e.g., telemetry system, communication protocol, student plan, security system, Web-based information system, investment, educational courses) illustrate the suggested aggregation approach.