In two recent publications, it was demonstrated that the nonlinear diffusion acceleration (NDA) algorithm, a moment-based accelerator, could be modified to accelerate the solution to neutron transport calculations with anisotropic scattering. It was demonstrated, however, that as the scattering became less isotropic, the performance of the algorithm degraded. Furthermore, it has been shown that Anderson acceleration (AA) could be used to speed up neutron transport and plasma physics calculations. In this paper, we combine these ideas to demonstrate that AA can be used to remedy the degraded performance of NDA when scattering is anisotropic. We describe each of the methods in detail and demonstrate the results on a series of fixed-source calculations and a pair of k-eigenvalue calculations.