We present the first complete spoken dialogue system driven by a multi-dimensional statistical dialogue manager. This framework has been shown to substantially reduce data needs by leveraging domain-independent dimensions, such as social obligations or feedback, which (as we show) can be transferred between domains. In this paper, we conduct a user study and show that the performance of a multi-dimensional system, which can be adapted from a source domain, is equivalent to that of a one-dimensional baseline, which can only be trained from scratch.