Rigid spherical microphone arrays (RSMAs) have been widely used in ambisonics sound field recording. While it is desired to combine the information captured by a grid of densely arranged RSMAs for expanding the area of accurate reconstruction, or sweet-spots, this is not trivial due to inter-array interference. Here we propose multiple scattering ambisonics, a method for three-dimensional ambisonics sound field recording using multiple acoustically interacting RSMAs. Numerical experiments demonstrate the sweet-spot expansion realized by the proposed method. The proposed method can be used with existing RSMAs as building blocks and opens possibilities including higher degrees-of-freedom spatial audio.