Surface-enhanced Raman optical activity (SEROA) is investigated theoretically for molecules near a metal nanoshell. For this purpose, induced molecular electric dipole, magnetic dipole, and electric quadrupole moments must all be included. The incident field and the induced multipole fields all scatter from the nanoshell, and the scattered waves can be calculated via extended Mie theory. It is straightforward in this framework to calculate the incident frequency dependence of SEROA intensities, i.e., SEROA excitation profiles. The differential Raman scattering is examined in detail for a simple chiroptical model that provides analytical forms for the relevant dynamical molecular response tensors. This allows a detailed investigation into circumstances that simultaneously provide strong enhancement of differential intensities and remain selective for molecules with chirality.