Model membranes consisting of pure lipid components have clearly advanced the understanding of biological cell membranes. However, the reconstitution of membrane proteins into model lipid bilayers is not straightforward and requires specific strategies for each protein system. In contrast, membranes of living cells have a complex composition with a multitude of different lipid components, proteins and sugars. In this work, we show that membrane blebs derived from the plasma membrane of living cells, also called giant plasma membrane vesicles, can be used to study the interaction of the membrane proteins CD47 and SIRPα, which are involved in immune signaling. Membrane blebs are an interesting model because they exhibit the compositional heterogeneity of the plasma membrane but their morphological behavior can still be described by a few parameters such as bending rigidity, reduced volume and tension. Specifically, we study the interaction of CD47 reconstituted in blebs and surface-immobilized SIRPα. Using this model system we explore membrane-mediated cooperative binding effects under different biologically relevant conditions. We find that acidic environment decreases the binding affinity of membrane-reconstituted CD47 to SIRPα. Finally, we discuss implications for in-vitro cancer models. Financial support from the Deutsche Forschungsgemeinschaft (DFG) via the IRTG 1524 is gratefully acknowledged.