Hardware overprovisioning is a widely used technique to improve the average power utilization of computing systems by capping the processor’s power consumption. However, applying a uniform power cap across multiprocessor system sockets can significantly impact co-running applications due to workload variations. This paper introduces KarmaPM, a novel power management library for co-running applications on multiprocessor systems, independent of the parallel programming model, based on application power donation phases. KarmaPM dynamically redistributes power bidirectionally across the sockets to improve overall system throughput for co-running applications while maintaining fairness between them. KarmaPM periodically profiles the CPU utilization of each application. When it detects an application underutilizing its CPU resources, it donates the surplus power from this donor application’s sockets to the other sockets (receivers), exhibiting high CPU utilization. When the donor application enters a high CPU utilization phase, KarmaPM employs a reward power scheme that rewards the donor application by returning a portion of the power transferred to the receiver sockets. We evaluated KarmaPM across various exascale proxy application mixes and power caps on a four-socket, 72-core Intel Cooper Lake processor. Our results show that KarmaPM improved the system throughput (geometric mean) by 13.2% at a lower power cap and 6.6% at a higher power cap. Additionally, KarmaPM delivered improvements of 12.5% and 4.4% in system throughput (geomean) compared to an existing power manager at these respective power caps.