Limited by the lower power of a solid oxide electrolyzer (SOE) stack, the scaling-up of the SOE technology requires multiple stacks to be integrated into a hotbox to form a multi-stack module (MSM). It is critical to guarantee the uniformity of stacks in an MSM, which has a prominent impact on its performance and durability. However, the thermo-fluid-electrical couplings between different stacks in an MSM are highly dependent on its structure and stack arrangement, which flowsheet models with lumped parameters cannot describe. This study proposes a three-dimensional (3D) multiphysics MSM model accelerated by the homogenization approach to investigate the MSM performances. By simplifying the stack structure using the homogenization method, the number of mesh elements is remarkably reduced, making it possible to complete the simulation of a four-stack MSM model within 3 min. Simulation shows that a 33% drop in maximum power and a 30 °C increase in temperature difference are induced by uneven gas distribution and unequal stack resistances for an MSM with serial electrical arrangement. It is also shown that the parallel arrangement is less susceptible to non-ideal factors than the serial arrangement, which enlightened the possibility of optimizing the stack arrangement to improve the MSM's performance.