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In solving today's social issues, it is necessary to determine solutions that are acceptable to all stakeholders and collaborate to apply them. The conventional technology of "permissive meeting analysis" derives a consensusable choice that falls within everyone's permissible range through mathematical analyses; however, it tends to be biased toward the majority in a group, making it difficult to reach a consensus when a conflict arises. To support consensus building (defined here as an acceptable compromise that not everyone rejects), we developed a composite consensus-building process. The developed process addresses this issue by combining permissible meeting analysis with a new "compromise choice-exploration" technology, which presents a consensusable choice that emphasizes fairness and equality among everyone when permissible meeting analysis fails to do so. When both permissible meeting analysis and compromise choice exploration do not arrive at a consensus, a facility is provided to create a sublated choice among those provided by them. The trial experimental results confirmed that permissive meeting analysis and compromise choice exploration are sufficiently useful for deriving consensusable choices. Furthermore, we found that compromise choice exploration is characterized by its ability to derive choices that control the balance between compromise and fairness. Our proposed composite consensus-building approach could be applied in a wide range of situations, from local issues in municipalities and communities to international issues such as environmental protection and human rights issues. It could also aid in developing digital democracy and platform cooperativism.