The paper presents two multilingual coreference resolution systems submitted for the CRAC Shared Task 2023. The DFKI-Adapt system achieves 61.86 F1 score on the shared task test data, outperforming the official baseline by 4.9 F1 points. This system uses a combination of different features and training settings, including character embeddings, adapter modules, joint pre-training and loss-based re-training. We provide evaluation for each of the settings on 12 different datasets and compare the results. The other submission DFKI-MPrompt uses a novel approach that involves prompting for mention generation. Although the scores achieved by this model are lower compared to the baseline, the method shows a new way of approaching the coreference task and provides good results with just five epochs of training.