Although many approaches have been developed to form robot coalitions that can achieve a multirobot task, no general methods exist to execute these coalitions, especially when the coordination among the robots is tightly coupled. In this paper, we propose a coordination mechanism as the first step to address coalition execution; it provides a flexible method to reason about synergies with overlapping coalitions (thus enabling multi-tasking robots in multi-robot tasks), which not only improves efficiency, but also reduces resource requirements in task execution. This means that our approach enables tasks that cannot be easily handled before, especially when critical resources are rare but commonly required. Our approach is based on the concept of sensor constraint, which is introduced by the tight coupling (e.g., information sharing) between the robots. We show that our algorithm is sound and complete in finding a coordination solution given a few assumptions, and discuss a distributed implementation. Simulation results are provided to demonstrate the capabilities of this new approach.