Previous powder diffraction studies of the superoxygenated La(2-x)Sr(x)CuO(4+y) (LSCO+O) system have not provided a model describing the superstructures of the intercalated oxygen recently observed in single crystal samples. It is believed that these superstructures are directly related to the unusual magnetic and superconducting (SC) properties of LSCO+O with T_N ~ T_c ~ 40 K regardless of Sr content. To our knowledge no previous attempt has been made to perform single crystal diffraction and refinement analysis on this system. We believe a full survey of these oxygen superstructures and concomitant displacement of surrounding elements is needed and best performed by broad q-range single crystal neutron Laue diffraction. We intend to collect superstructure peaks and refine the data for 4 specific temperatures relating to the superstructures of LSCO+O in order to obtain a good model.