A hierarchical control architecture is proposed for the optimal day-ahead commitment of multiple grid support services within a virtual power plant (VPP). The day-ahead optimization considers pricing and cost data to determine the commitment schedule, and a robust Model Predictive Control (MPC) approach is included to minimize the unbalance fees during real-time operations. The multi-level control has been demonstrated experimentally using a hybrid test system, where the VPP is formed of a commercial 240 kW, 180 kWh battery energy storage system (BESS), while the additional assets are modelled in a real-time digital simulator (RTDS). Two case studies are analyzed: the first assumes a purely-electrical VPP, with a single connection to the public network; the second involves a multi-energy approach, with the introduction of a gas-supplied Combined Heat and Power unit (CHP). Both winter and summer price scenarios are tested. The results show the superiority of the multiple-service operation compared to providing a single grid support service. For example, the net revenue is increased by 30% (winter) and 7% (summer) when compared to just frequency regulation, and by +99% (winter) and 30% (summer) when compared to only energy arbitrage.