The chain graph representations of an achievable scheme is a recently introduced theoretical tool to derive achievable regions based on superposition coding and binning for a general, single-hop, multi-terminal network. It allows for a compact representation of complex transmission strategies and the derivation of the corresponding achievable region for a large class of channels. In this paper we extend the original concept to include a new random coding technique that generalizes superposition coding and binning. With this coding strategy, one generates a top codebook conditionally dependent on the bottom codeword and successively uses binning to impose a different conditional distribution between top and bottom codewords. The region achieved with this strategy relates to the Kullback-Leibler divergence between the distribution of the codewords at generation and the distribution after binning.