Cylindrical and spherical （nonplanar） solitary waves （SWs） and double layers （DLs） in a multi-ion plasma system （containing inertial positively as well as negatively charged ions, non-inertial degenerate electrons, and negatively charged static dust） are studied by employing the standard reductive perturbation method. The modified Gardner （MG） equation describing the nonlinear propagation of the dust ion-acoustic （DIA） waves is derived, and its nonplanar SWs and DLs solutions are numerically analyzed. The parametric regimes for the existence of SWs, which are associated with both positive and negative potential, and DLs which are associated with negative potential, are obtained. The basic features of nonplanar DIA SWs, and DLs, which are found to be different from planar ones, are also identified.