Using a helium ion hitting various metal surfaces as a model system, we describe a general quantum-kinetic approach for calculating ion-induced secondary electron emission spectra at impact energies where the emission is driven by the internal potential energy of the ion. It is based on an effective model of the Anderson-Newns-type for the subset of electronic states of the ion-surface system most strongly affected by the collision. Central to our approach is a pseudo-particle representation for the electronic configurations of the projectile which enables us, by combining it with two additional auxiliary bosons, to describe in a single Hamiltonian emission channels involving electronic configurations with different internal potential energies. It is thus possible to treat Auger neutralization of the ion on an equal footing with Auger de-excitation of temporarily formed radicals and/or negative ions. From the Dyson equations for the projectile propagators and an approximate evaluation of the selfenergies rate equations are obtained for the probabilities with which the projectile configurations occur and an electron is emitted in the course of the collision. Encouraging numerical results, especially for the helium-tungsten system, indicate the potential of our approach.