Recent statistical approaches have improved the robustness and scalability of spoken dialogue systems. However, despite recent progress in domain adaptation, their reliance on in-domain data still limits their cross-domain scalability. In this paper, we argue that this problem can be addressed by extending current models to reflect and exploit the multi-dimensional nature of human dialogue. We present our multi-dimensional, statistical dialogue management framework, in which transferable conversational skills can be learnt by separating out domain-independent dimensions of communication and using multi-agent reinforcement learning. Our initial experiments with a simulated user show that we can speed up the learning process by transferring learnt policies.