We propose a method that can record extended sound fields generated by sound sources with arbitrary directivity. Sound field recordings given as a spherical harmonic expansion are valid within a region limited by the highest expansion order. In current methods, multiple spherical microphone arrays are used for recording sound fields over large regions. Previously, we proposed a method to take advantage of the approximate knowledge of the sound source position to synthesize sound field anywhere in space from a single microphone array recording using a translation operator. This method assumes only omni-directional sound sources in the definition of the translation operator. The present research deals with the problem of extending previous results to sound sources with arbitrary radiation directivity patterns. A new translation operator is calculated taking into account that complex sound sources can be approximated as a collection of multipoles. The results of numerical simulations and actual measurements show that the proposed multipole translation operator can effectively synthesize extended sound field information from a single spherical microphone array recording.