Clathrin-coated pits are formed by the recognition of membrane and cargo by the heterotetrameric AP2 complex and the subsequent recruitment of clathrin triskelia. A potential role for AP2 in coated-pit assembly beyond initial clathrin recruitment has not been explored. Clathrin binds the β2 subunit of AP2, and several binding sites on β2 and on the clathrin heavy chain have been identified, but our structural knowledge of these interactions is incomplete and their functional importance during endocytosis is unclear. Here, we analysed the cryo-EM structure of clathrin cages assembled in the presence of β2 hinge and appendage (β2HA) domains. We find that the β2-appendage binds in at least two positions in the cage, demonstrating that multi-modal binding is a fundamental property of clathrin-AP2 interactions. In one position, β2-appendage cross-links two adjacent terminal domains from different triskelia below the vertex. Functional analysis of β2HA-clathrin interactions reveals that endocytosis requires two clathrin interaction sites: a clathrin-box motif on the hinge and the “sandwich site” on the appendage, with the appendage “platform site” having less importance. From these studies and the work of others, we propose that β2-appendage binding to more than one clathrin triskelion is a key feature of the system and likely explains why clathrin assembly is driven by AP2.