2015 IEEE. We propose an achievable decode-forward rate region for the two-way multi-relay network. The region is the outcome of a carefully mediated attempt, through a so-called "reverse-order" ranking policy, to privilege the disadvantaged nodes in the network over the advantaged. We use the word "advantage" in reference to the ability of a node to recover the decode-forward outer-bound by virtue of its position in the network. The proposed rate-region shows promise in recovering most of a decode-forward outer-bound which, due to a fundamental deadlock problem we identify, is not tight. The rate region itself is derived from (n-2)! individual regions, each corresponding to a unique decode-forward scheme, which geometrically fit together into an intelligible whole. The underlying theory, offset encoding, appears to be well suited for multi-source multi-relay networks with bidirectional information flow.