The strategy of enhancing molecular recognition by improving the binding affinity of drug molecules against targets has generated a lot of successful therapeutic applications. However, one critical consequence of such affinity improvement, generally called "on-target, off-tumor" toxicity, emerged as a major obstacle limiting their clinical usage. Herein, we provide a modular assembly strategy that affords affinity-tunable DNA nanostructures allowing for immobilizing multiple aptamers that bind to the example antigen of EpCAM with different affinities. We develop a theoretical model proving that the apparent affinity of aptamer assemblies to target cells varies with antigen density as well as aptamer valency. More importantly, we demonstrate experimentally that the theoretical model can be used to predict the least valency required for discrimination between EpCAM high and EpCAM low cells in vitro and in vivo. We believe that our strategy will have broad applications in an engineering nucleic acid-based delivery platform for targeted and cell therapy.