A general formalism is developed to construct and solve a system of linearized moment equations for parallel and perpendicular closures in high-collisionality plasmas. It is applicable for multiple ion species with arbitrary masses, temperatures, charges, and densities. The convergence of closure coefficients is evaluated by increasing the number of moments from 2 to 32 for scalar, vector, and rank-2 tensor moments. As an example, the complete set of closure coefficients for a deuterium-carbon plasma over the entire Hall parameter range is presented. The closure coefficients at various temperature ratios show that the one-temperature closure coefficients can differ significantly from the two-temperature coefficients.