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We investigate the potential of mutual scattering, i.e., light scattering with multiple properly phased incident beams, as a method to extract structural information from inside an opaque object. In particular, we study how sensitively the displacement of a single scatterer is detected in an optically dense sample of many (up to $N=1000$) similar scatterers. By performing exact calculations on ensembles of many point scatterers, we compare the mutual scattering (from two beams) and the well-known differential cross-section (from one beam) in response to the change of location of a single dipole inside a configuration of randomly distributed similar dipoles. Our numerical examples show that mutual scattering provides speckle patterns with an angular sensitivity at least 10 times higher than the traditional one-beam techniques. By studying the "susceptivity" of mutual scattering, we demonstrate the possibility to determine the original depth relative to the incident surface of the displaced dipole in an opaque sample. Furthermore, we show that mutual scattering offers a new approach to determine the complex scattering amplitude.