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This paper discusses the Integrated Plasma Simulator (IPS), a framework for coupled multiphysics simulation of fusion plasmas, in the context of many-task computing. The IPS supports multiple levels of parallelism: individual computational tasks can be parallel, components can launch multiple tasks concurrently, tasks from multiple components can be executed concurrently within a simulation, and multiple simulations can be run simultaneously. Each level of parallelism is constructed on top of the many-task computing capabilities implemented in the IPS, the foundation for the parallelism presented at the multiple simulation level. We show that a modest number of simultaneous simulations, with appropriately sized resource allocations, can provide a better trade-off between resource utilization and overall execution time than if they are run as separate jobs. This approach is highly beneficial for situations in which individual simulation tasks may differ significantly in parallel scalability, as is the case in many scientific communities where coupled simulations rely substantially on legacy code.