This paper investigates the use of a general multi-arm multi-stage (MAMS) approach for time-to-event outcomes that would streamline simultaneous comparison of a large number of promising therapies in clinical trials, thus significantly reducing the time and the number of patients needed to evaluate the treatment. Controlling type I error in this setting is different than regular clinical trials as this approach incorporates both multiple comparison between arms and multiple stages. Historically, pairwise (PWER) and familywise (FWER) type I error rates have been primarily used to regulate the type I error in such designs. This paper will focus on constructing the efficacy and futility boundaries for a MAMS clinical trial in two different scenarios. In the first, it is assumed that the same outcome is used throughout the clinical trial for both intermediate and final assessments. In this scenario, we propose using the generalized Dunnett procedure that controls FWER. In the latter scenario, where intermediate and final outcomes are different in nature, we propose modifications to the existing method that originally concentrated on controlling PWER and extend the method to include FWER in the design. We also explore the performance of the proposed MAMS design in a setting where the proportional hazard assumption is violated in the presence of a delayed treatment effect and demonstrate the loss of power because of that. An alternative test statistic that can help circumvent this problem to maintain the desired power is also suggested.