The growing availability of multi-source ocean remote sensing data is a key factor for improving our understanding of upper ocean dynamics, ocean circulation and atmospheric-ocean interactions. Following an ongoing body of work that investigates mesoscale upper ocean dynamics from linear couplings between SST (sea surface temperature) and SSH (sea surface height), we propose a novel observation-driven framework for the identification and characterization of sea surface dynamical modes. It relies on a multi-modal decomposition of SST-SSH relationships. Our findings suggest that upper ocean dynamics may be decomposed as the superimposition of several dynamical modes, rather than mutually exclusive ones as investigated in previous work. Our study stresses the relevance of a non-negative bi-modal additive decomposition to capture the complex space-time variability of mesoscale upper ocean dynamics.