Damping service provision through VSC-based HVDC links has been extensively covered in the literature. However, little or no attention has been paid to the available range of active and reactive power modulation when the HVDC link is already operating at rated capacity. In these conditions some overload capability is usually assumed, ignoring the physical constraints imposed by the safe operating area of the IGBT modules in the converter. This paper presents, in a unified framework, the provision of damping support from VSC-HVDC links equipped with additional control for short-term overload capability. The performance of a Model Predictive Control (MPC) damping controller that accounts for the extended P/Q operating area of the converter is analysed. Case studies are presented to show that the extracted short-term overload capability can significantly improve the damping support from VSC-HVDC links. Simulation results also include the impact of damping control action on the junction temperatures of the IGBT modules of the converters, quantifying the effect of this service on the semiconductor temperature dynamics.