The process of screening agents one-at-a-time under the current clinical trials system suffers from several deficiencies that could be addressed in order to extend financial and patient resources. In this article, we introduce a statistical framework for designing and conducting randomized multi-arm screening platforms with binary endpoints using Bayesian modeling. In essence, the proposed platform design consolidates inter-study control arms, enables investigators to assign more new patients to novel therapies, and accommodates mid-trial modifications to the study arms that allow both dropping poorly performing agents as well as incorporating new candidate agents. When compared to sequentially conducted randomized two-arm trials, screening platform designs have the potential to yield considerable reductions in cost, alleviate the bottleneck between phase I and II, eliminate bias stemming from inter-trial heterogeneity, and control for multiplicity over a sequence of a priori planned studies. When screening five experimental agents, our results suggest that platform designs have the potential to reduce the mean total sample size by as much as 40% and boost the mean overall response rate by as much as 15%. We explain how to design and conduct platform designs to achieve the aforementioned aims and preserve desirable frequentist properties for the treatment comparisons. In addition, we demonstrate how to conduct a platform design using look-up tables that can be generated in advance of the study. The gains in efficiency facilitated by platform design could prove to be consequential in oncologic settings, wherein trials often lack a proper control, and drug development suffers from low enrollment, long inter-trial latency periods, and an unacceptably high rate of failure in phase III.