In phase II platform trials, 'many-to-one' comparisons are performed when K experimental treatments are compared with a common control to identify the most promising treatment(s) to be selected for Phase III trials. However, when sample sizes are limited, such as when the disease of interest is rare, only a single Phase II/III trial addressing both treatment selection and confirmatory efficacy testing may be feasible. In this paper, we suggest a two-step safety selection and testing procedure for such seamless trials. At the end of the study, treatments are first screened on the basis of safety, and those deemed to be sufficiently safe are then taken forwards for efficacy testing against a common control. All safety and efficacy evaluations are therefore performed at the end of the study, when for each patient all safety and efficacy data are available. If confirmatory conclusions are to be drawn from the trial, strict control of the family-wise error rate (FWER) is essential. However, to avoid unnecessary losses in power, no type I error rate should be "wasted" on comparisons which are no longer of interest because treatments have been dropped due to safety concerns. We investigate the impact on power and FWER control of multiplicity adjustments which correct efficacy tests only for the number of safe selected treatments instead of adjusting for all K null hypotheses the trial begins testing. We derive conditions under which strict control of the FWER can be achieved. Procedures using the estimated association between safety and efficacy outcomes are developed for the case when the correlation between endpoints is unknown. The operating characteristics of the proposed procedures are assessed via simulation.