The single-site Anderson model with degeneracy ${N}_{f}$ is solved for the case in which the lowest eigenstate contains $L$ electrons in the $f$ orbital, where $0lLl{N}_{f}.$ The noncrossing approximation is used to find the density of states including the Kondo resonance. The Seebeck coefficient is calculated as a function of temperature for every value of $L$. We find that the Seebeck coefficient is largest for $L=1$ and declines in value as $L$ increases. This suggests that large Seebeck coefficients are not possible in mixed-valent systems besides those of cerium or ytterbium.