Anaphora resolution (coreference) systems designed for the CONLL 2012 dataset typically cannot handle key aspects of the full anaphora resolution task such as the identification of singletons and of certain types of non-referring expressions (e.g., expletives), as these aspects are not annotated in that corpus. However, the recently released dataset for the CRAC 2018 Shared Task can now be used for that purpose. In this paper, we introduce an architecture to simultaneously identify non-referring expressions (including expletives, predicative s, and other types) and build coreference chains, including singletons. Our cluster-ranking system uses an attention mechanism to determine the relative importance of the mentions in the same cluster. Additional classifiers are used to identify singletons and non-referring markables. Our contributions are as follows. First all, we report the first result on the CRAC data using system mentions; our result is 5.8% better than the shared task baseline system, which used gold mentions. Second, we demonstrate that the availability of singleton clusters and non-referring expressions can lead to substantially improved performance on non-singleton clusters as well. Third, we show that despite our model not being designed specifically for the CONLL data, it achieves a score equivalent to that of the state-of-the-art system by Kantor and Globerson (2019) on that dataset.