There is a growing interest in the implementation of platform trials, which provide the flexibility to incorporate new treatment arms during the trial and the ability to halt treatments early based on lack of benefit or observed superiority. In such trials, it can be important to ensure that error rates are controlled. This paper introduces a multi-stage design that enables the addition of new treatment arms, at any point, in a preplanned manner within a platform trial, while still maintaining control over the family-wise error rate. This paper focuses on finding the required sample size to achieve a desired level of statistical power when treatments are continued to be tested even after a superior treatment has already been found. This may be of interest if there are treatments from different sponsors which are also superior to the current control or multiple doses being tested. The calculations to determine the expected sample size is given. A motivating trial is presented in which the sample size of different configurations is studied. In addition, the approach is compared to running multiple separate trials and it is shown that in many scenarios if family-wise error rate control is needed there may not be benefit in using a platform trial when comparing the sample size of the trial.