Ligand/receptor multivalent interactions have been exploited to drive self-assembly of nanoparticles, hard colloids, and, more recently, compliant units including emulsion droplets and lipid vesicles. In deformable liposomes, formation of links between two membranes produces morphological changes depending on the amount of ligands in the environment. Here, we study a proof-of-concept biosensing system in which single lipid vesicles adhere to a flat supported lipid bilayer, both decorated with membrane-anchored biotinylated receptors. Adhesion is driven by multivalent streptavidin (SA) ligands forming bridges between the vesicles and the supported bilayer. Upon changing the concentration of ligands, we characterize the morphological and mechanical changes of the vesicles, including the formation of a stable adhesion patch, membrane tension, and the kinetics of bridge rupture/formation. We observe vesicle binding only within a specific range of ligand concentrations: adhesion does not occur if the amount of SA is either too low or too high. A theoretical model is presented, elucidating the mechanism underlying this observation, particularly, the role of SA multivalency in determining the onset of adhesion. We elaborate on how the behavior of membranes studied here could be exploited in next-generation (bio)molecular analytical devices.