In this paper we propose a new hybrid technique to suppress range ambiguities in spaceborne SAR systems with multiple elevation beams. First, conventional scan-on-receive (SCORE) is performed in real-time onboard the satellite by employing a set of dispersive beams that maximize the collected signal energy for each transmitted pulse. The range ambiguities are then removed in a second step by a joint processing of the signals collected by the multiple elevation beams. The suggested two-stage approach has the advantage that a more robust range ambiguity suppression, which may involve advanced nulling techniques to account for local topography as well as satellite attitude and instrument phase errors, can be performed on ground without tremendously increasing the onboard processing demands or the data downlink volume.