Organizations faces significant challenges in decision-making, due to the complexity of managing contradictory logics simultaneously. This study leverages paradox theory to explore how organizations confront with more than two logics. Drawing on four-year ethnographic study of innovation projects within Italian local government agencies, we reveal that actors tend to oversimplify the three competing logics they face—legal, performance, and democratic responsiveness—into dyadic tensions. This oversimplification neglects the "three-body problem", where the compresence of three poles challenge innovation attempts. Our findings advance paradox literature by demonstrating that organizations may encounter three-poles paradoxes. In such cases, navigating these complexities requires the adoption of a strong process logic, a necessity that traditional two-pole paradoxes may not demand. We highlight the implications of multipolar paradoxes for theory and practice, providing new insights into fostering innovation in environments of high complexity.