We calculate the time-dependent nonlinear transport current through an interacting quantum dot in the single-electron tunneling (SET) regime. We show that an additional dc current is generated by the electron-electron interaction by adiabatic out-of-phase modulation of the gate and bias voltage. This current can arise only when two SET resonance conditions are simultaneously satisfied. We propose an adiabatic transport spectroscopy where lock-in measurement of a "time-averaged stability diagram" probes interactions, tunnel asymmetries, and changes in the ground state spin degeneracy.