This paper extends the conventional single-stage additive manufacturing (AM) processes to multi-STage distRibutEd AM systems (STREAMs). In STREAM, a batch of material produced at the pre-processing stage is jointly consumed by distributed AM printers, and then the printed parts are collected for the centralized post-processing. Such systems are widely encountered in AM processes such as energy-AM, metal-AM and bio-AM. Modeling and managing such complex systems have been challenging. We propose a novel framework for 'cyber-coordinated simulation' to manage the hierarchical information in STREAM. This is important because simulation can be used to infuse data into predictive analytics, thus providing guidance for the optimization and control of STREAM operations. The proposed framework is hierarchical in nature, where single stage, multi-stage and distributed productions are modeled through the integration of different simulators. We demonstrate the proposed framework with simulation data from freeze nano printing AM processes.