We present our PDTB-style annotations on conversational Twitter data, which was initially annotated by Scheffler et al. (2019). We introduced 1,043 new annotations to the dataset, nearly doubling the number of previously annotated discourse relations. Subsequently, we applied a neural Shallow Discourse Parsing (SDP) model to the resulting corpus, improving its performance through retraining with in-domain data. The most substantial improvement was observed in the sense identification task (+19%). Our experiments with diverse training data combinations underline the potential benefits of exploring various data combinations in domain adaptation efforts for SDP. To the best of our knowledge, this is the first application of Shallow Discourse Parsing on Twitter data