The magnitude of an acoustic point source is traditionally described as monopole, dipole, or higher-order multipole source strengths. The polarizability tensor, commonly used in electromagnetics, can be used to describe the scattering from an acoustically small heterogeneity in a background medium as monopole, dipole, and higher order multipoles due to the pressure and particle velocity at the scattering site. Recent research on bianisotropic acoustic (or Willis) metamaterials has employed the acoustic polarizability tensor as a convenient descriptor of the scattered fields from scatterers with asymmetries since non-zero off-diagonal terms indicate the existence and relative strength of Willis coupling. In the present work, we employ the polarizability tensor in a multiple scattering formulation for N arbitrary, point scatterers. The polarizability tensor for an example scatterer is extracted from finite element simulations by generalizing the approach of Su and Norris [Phys. Rev. B 98, 174305, (2018)]. We then provide a metasurface example to demonstrate the ability of the multiple scattering approach to consider variability in scatterer position and orientation in the calculation of the total scattered field.