Incivility is a problem on social media, and it comes in many forms (name-calling, vulgarity, threats, etc.) and domains (microblog posts, online news comments, Wikipedia edits, etc.). Training machine learning models to detect such incivility must handle the multi-label and multi-domain nature of the problem. We present a BERT-based model for incivility detection and propose several approaches for training it for multi-label and multi-domain datasets. We find that individual binary classifiers outperform a joint multi-label classifier, and that simply combining multiple domains of training data outperforms other recently-proposed fine tuning strategies. We also establish new state-of-the-art performance on several incivility detection datasets.