<p>In multiple treatment comparison in clinical trials, patients typically arrive sequentially, and they are assigned to one of the competing treatments using some randomized allocation rules that are often response-adaptive in nature. Our objective is to determine the treatments that are superior or inferior to the control, which leads to testing multiple hypotheses under the response-adaptive design framework. We develop two novel test procedures to control the probabilities of at least one false rejection (FWER-I) and at least one false acceptance (FWER-II) at prefixed levels. The allocation rules in our procedures minimize some appropriate cost functions, namely the expected number of treatment failures or the total sample sizes. We prove that our procedures terminate sampling in finite times and control both FWER-I and FWER-II asymptotically as the difference between the null and alternative hypotheses vanishes. Superiority of the proposed procedures are validated through detailed analyses of real and simulated datasets.</p>