Fluid moment models are a popular option when modeling rarefied gases, primarily due to their computational advantage over kinetic models. They also provide an advantage over traditional equilibrium ‘5-moment’ fluid models (density, velocity, isotropic temperature) by retaining more information about the fluid velocity distribution function (VDF) through its moments. These higher-order moment models are able to capture finite non-equilibrium kinetic effects through the additional moments. One non-equilibrium effect of particular interest is anisotropic pressure. A full pressure tensor directly modifies momentum transport and has down-stream effects on mass and energy transport as well. In plasmas, anisotropic pressure is common in regions with strong magnetic fields, as transport across field lines is suppressed. Likewise, plasma-wall interactions and different populations of particles interacting can generate pressure anisotropy. Previous work has employed 13-moment (density, velocity, anisotropic pressure, heat flux) and 14-moment models (13 + 4th order moment) to great success in reconstructing kinetic VDFs and capturing anisotropy, but we would like to revisit 10-moment models (density, velocity, anisotropic pressure) for their relative simplicity as the minimal models which can capture a full pressure tensor. In this study, we present results from the development of a 10-moment multi-fluid model with Chapman-Enskog closure for heat flux. The model is benchmarked for neutral fluids on classic shock tube test problems in 1 and 2 dimensions. The code is applied to a cross-field plasma discharge in a simplified Hall effect thruster discharge chamber geometry. Finally, we will also present results demonstrating the ability of our 10-moment model to capture the Weibel instability, a traditionally fully kinetic phenomenon. Our results are compared with a 5-moment fluid model, kinetic Particle-in-Cell Monte Carlo Collision and Direct Simulation Monte Carlo codes and we demonstrate a good degree of agreement.