To meet the ever-increasing demand for energy storage and power supply, battery systems are being vastly applied to, e.g., grid-level energy storage and automotive traction electrification. In pursuit of safe, efficient, and cost-effective operation, it is critical to predict the maximum acceptable battery power on the fly, commonly referred to as the battery system's state of power (SoP). As compared to the SoP prediction at the battery cell level, predicting the SoP of a multi-battery system, especially including parallel-connected cells/modules/packs, is much more complicated and far less investigated. To solve this problem, a system-model-based SoP prediction method is first proposed in this paper. Specifically, based on the formulated system model and generic state-space representation, the challenge of nonmonotonic system state evolution, arising from the dynamic parallel current distribution, is identified and systematically addressed by the proposed method. As demonstrated by tests on a battery system set up with experimentally verified parameter values, the proposed method outperforms the commonly applied cell-SoP based methods for providing a more accurate and reliable prediction of the battery system SoP. Moreover, the proposed prediction framework presented in generic forms can be readily applied to other system structures.