Screening trials are small trials used to decide whether an intervention is sufficiently promising to warrant a large confirmatory trial. Previous literature examined the situation where treatments are tested sequentially until one is considered sufficiently promising to take forward to a confirmatory trial. An important consideration for sponsors of clinical trials is how screening trials should be planned to maximize the efficiency of the drug development process. It has been found previously that small screening trials are generally the most efficient. In this paper we consider the design of screening trials in which multiple new treatments are tested simultaneously. We derive analytic formulae for the expected number of patients until a successful treatment is found, and propose methodology to search for the optimal number of treatments, and optimal sample size per treatment. We compare designs in which only the best treatment proceeds to a confirmatory trial and designs in which multiple treatments may proceed to a multi-arm confirmatory trial. We find that inclusion of a large number of treatments in the screening trial is optimal when only one treatment can proceed, and a smaller number of treatments is optimal when more than one can proceed. The designs we investigate are compared on a real-life set of screening designs.