Multi-Arm Multi-Stage (MAMS) designs can notably improve efficiency in later stages of drug development, but they can be suboptimal when an order in the effects of the arms can be assumed. In this work, we propose a Bayesian multi-arm multi-stage trial design that selects all promising treatments with high probability and can efficiently incorporate information about the order in the treatment effects as well as incorporate prior knowledge on the treatments. A distinguishing feature of the proposed design is that it allows taking into account the uncertainty of the treatment effect order assumption and does not assume any parametric arm-response model. The design can provide control of the family-wise error rate under specific values of the control mean and we illustrate its operating characteristics in a study of symptomatic asthma. Via simulations, we compare the novel Bayesian design with frequentist multi-arm multi-stage designs and a frequentist order restricted design that does not account for the order uncertainty and demonstrate the gains in the sample sizes the proposed design can provide. We also find that the proposed design is robust to violations of the assumptions on the order.