As the popularity of 3D printing or additive manufacturing (AM) continues to increase for use in commercial and defense supply chains, the requirement for reliable, robust protection from adversaries has become more important than ever. Three-dimensional printing security focuses on protecting both the individual Industrial Internet of Things (I-IoT) AM devices and the networks that connect hundreds of these machines together. Additionally, rapid improvements in quantum computing demonstrate a vital need for robust security in a post-quantum future for critical AM manufacturing, especially for applications in, for example, the medical and defense industries. In this paper, we discuss the attack surface of adversarial data manipulation on the physical inter-device communication bus, Controller Area Network (CAN). We propose a novel, hierarchical tree solution for a secure, post-quantum-supported security framework for CAN-based AM devices. Through using subnet hopping between isolated CAN buses, our framework maintains the ability to use legacy or third-party devices in a plug-and-play fashion while securing and minimizing the attack surface of hardware Trojans or other adversaries. The results of the physical implementation of our framework demonstrate 25% and 90% improvement in message costs for authentication compared to existing lightweight and post-quantum CAN security solutions, respectively. Additionally, we performed timing benchmarks on the normal communication (hopping) and authentication schemes of our framework.