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One simplifying assumption made in distributed robot systems is that the robots are single-tasking: each robot operates on a single task at any time. While such a sanguine assumption is innocent to make in situations with sufficient resources so that the robots can operate independently, it becomes impractical when they must share their capabilities. In this paper, we consider multi-tasking robots with multi-robot tasks. Given a set of tasks, each achievable by a coalition of robots, our approach allows the coalitions to overlap and task synergies to be exploited by reasoning about the physical constraints that can be synergistically satisfied for achieving the tasks. The key contribution of this work is a general and flexible framework to achieve this ability for multi-robot systems in resource-constrained situations to extend their capabilities. The proposed approach is built on the information invariant theory, which specifies the interactions between information requirements. In our work, we map physical constraints to information requirements, thereby allowing task synergies to be identified via the information invariant framework. We show that our algorithm is sound and complete under a problem setting with multi-tasking robots. Simulation results show its effectiveness under resource-constrained situations and in handling challenging situations in a multi-UAV simulator.