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Multi-arm clinical trials use a single control arm to evaluate multiple experimental treatments. In most cases this feature makes multi-arm studies considerably more efficient than two-arm studies. A bottleneck for implementation of a multi-arm trial is the requirement that all experimental treatments have to be available at the enrollment of the first patient. New drugs are rarely at the same stage of development. These limitations motivate our study of statistical methods for adding new experimental arms after a clinical trial has started enrolling patients. We consider both balanced and outcome-adaptive randomization methods for experimental designs that allow investigators to add new arms, discuss their application in a tuberculosis trial, and evaluate the proposed designs using a set of realistic simulation scenarios. Our comparisons include two-arm studies, multi-arm studies, and the proposed class of designs in which new experimental arms are added to the trial at different time points.