We extend the original entity-based coherence model (Barzilay and Lapata, 2008) by learning from more fine-grained coherence preferences in training data. We associate multiple ranks with the set of permutations originating from the same source document, as opposed to the original pairwise rankings. We also study the effect of the permutations used in training, and the effect of the coreference component used in entity extraction. With no additional manual annotations required, our extended model is able to outperform the original model on two tasks: sentence ordering and summary coherence rating. .