Membrane patterning is essential for signal transduction and regulation of forces driving many processes, including cell movement and adhesion. Over time, a few mechanisms responsible for the formation of protein domains were identified. However, the complex membranes, which host multiple protein and lipid types while being shaped by active processes, have proven to be a major challenge for both experimental reconstitutions in non-equilibrium settings and for conceptualization using theoretical models. We here hypothesize that the multi-lipid and multi-protein complexity of these membranes creates a framework for self-organization through membrane-mediated interactions. Additionally, we propose that cellular processes further enhance domain formation by stresses that couple to the local membrane composition. To test these hypotheses, we leverage the very successful collaboration of A. Smith at RBI Zagreb and K. Sengupta in Marseille. Building on its expertise in statistical physics, biophysics, analytical and computational modeling, the RBI team will utilize insights from K. Sengupta's experiments involving a unique model system—active giant unilamellar vesicles built from several lipids and hosting cadherins as well as integrins, encapsulating actin turnover. These experiments will motivate the construction of a theoretical framework for the patterning of complex, active membranes. This will involve the development of non-equilibrium physics concepts to calculate the phase diagrams of the passive and active complex systems. Furthermore, grounded in formal coarse-graining strategies, we will upscale our approaches to explore how activity influences membrane organization, cell shape changes, adhesion, and motility, as observed in experiments with cell models provided by an RBI collaborator I. Weber. Ultimately, this research will lead to a significantly deeper understanding of the origins of complex membrane patterning and its consequences on cell function.