Graph neural networks have emerged as a potent class of neural networks capable of leveraging the connectivity and structure of real-world graphs to learn intricate properties and relationships between nodes. Many real-world graphs exceed the memory capacity of a GPU due to their sheer size, and using GNNs on them requires techniques such as mini-batch sampling to scale. However, this can lead to reduced accuracy in some cases, and sampling and data transfer from the CPU to the GPU can also slow down training. On the other hand, distributed full-graph training suffers from high communication overhead and load imbalance due to the irregular structure of graphs. We propose Plexus, a three-dimensional (3D) parallel approach for full-graph training that tackles these issues and scales to billion-edge graphs. Additionally, we introduce optimizations such as a permutation scheme for load balancing, and a performance model to predict the optimal 3D configuration. We evaluate Plexus on several graph datasets and show scaling results for up to 2048 GPUs on Perlmutter, which is 33% of the machine, and 2048 GCDs on Frontier. Plexus achieves unprecedented speedups of 2.3x-12.5x over existing methods and a reduction in the time to solution by 5.2-8.7x on Perlmutter and 7-54.2x on Frontier.