Future Exascale systems will feature massive parallelism, manycore processors and heterogeneous architectures. In this scenario, it is increasingly difficult for HPC applications to fully and efficiently utilize the resources in system nodes. Moreover, the increased parallelism exacerbates the effects of existing inefficiencies in current applications. Research has shown that co-scheduling applications to share system nodes instead of executing each application exclusively can increase resource utilization and efficiency. Nevertheless, the current oversubscription and co-location techniques to share nodes have several drawbacks which limit their applicability and make them very application-dependent.This paper presents co-execution through system-wide scheduling. Co-execution is a novel fine-grained technique to execute multiple HPC applications simultaneously on the same node, outperforming current state-of-the-art approaches. We implement this technique in nOS-V, a lightweight tasking library that supports coexecution through system-wide task scheduling. Moreover, nOS-V can be easily integrated with existing programming models, requiring no changes to user applications. We showcase how co-execution with nOS-V significantly reduces schedule makespan for several applications on single node and distributed environments, outperforming prior node-sharing techniques.