While coreference resolution typically involves various linguistic challenges, recent models are based on a single pairwise scorer for all types of pairs. We present LingMess, a new coreference model that defines different categories of coreference cases and optimize multiple pairwise scorers, where each scorer learns a specific set of linguistic challenges. Our model substantially improves pairwise scores for most categories and outperforms cluster-level performance on Ontonotes and 5 additional datasets. Our model is available in https://github.com/shon-otmazgin/lingmess-coref