Microgrid installations have regained significant interest, driven by the increasing adoption of distributed energy resources, decentralized controls, and ongoing technological advancements. While the number of microgrids increases, there are opportunities to coordinate networks of microgrids. In this study, Irving’s algorithm is applied to a framework for the coordinated self-assembly of networked microgrids. Compared with the authors’ previous work, this new study relaxes the constraint on participated microgrids to have a single global objective. Thus, each microgrid can rank others according to its local preference. This reduces the amount of shared information, improves the privacy, and enhances the flexibility. In addition, the proposed method has better performance compared to the consensus method employed in the authors’ previous work, when dealing with a substantially larger number of microgrids exploring interconnection possibilities. The adaptability to that proposed framework is maintained. Examples are presented to illustrate the networking processes and self-assembly operations.