Multisatellite measurements of altimeter-derived sea surface height (SSH) have provided a wealth of information on the ocean. Yet, horizontal scales below 100 km remain scarcely resolved. Especially, in the Mediterranean Sea, an important fraction of the mesoscale range, characterized by a small Rossby radius of deformation of 15-20 km, is not properly retrieved by altimeter-derived gridded products. Here, we investigate a novel processing of AVISO products with a view to resolving the horizontal scales sensed by current along-track altimeter data. The key feature of our framework is the use of linear convolutional operators to model the fine-scale SSH detail as a function of different sea surface fields, especially optimally interpolated SSH and sea surface temperature (SST). The proposed model embeds the surface quasi-geostrophic SST-SSH synergy as a special case. Using an observing system simulation experiment with simulated SSH data from model outputs in the Western Mediterranean Sea, we show that the proposed approach has the potential for improving current optimal interpolations of gridded altimeter-derived SSH fields by more than 20% in terms of relative SSH and kinetic energy mean square error, as well as in terms of spectral signatures for horizontal scales ranging from 30 to 100 km. Our results also suggest that SST-SSH relationship may only play a secondary role compared with the interscale SSH cascade. We further discuss the relevance of the proposed approach in the context of future altimetric satellite missions.