The successful analysis of argumentative techniques in user-generated text is central to many downstream tasks such as political and market analysis. Recent argument mining tools use state-of-the-art deep learning methods to extract and annotate argumentative techniques from various online text corpora, but each task is treated as separate and different bespoke models are fine-tuned for each dataset. We show that different argument mining tasks share common semantic and logical structure by implementing a multi-task approach to argument mining that meets or exceeds performance from existing methods for the same problems. Our model builds a shared representation of the input and exploits similarities between tasks in order to further boost performance via parameter-sharing. Our results are important for argument mining as they show that different tasks share substantial similarities and suggest a holistic approach to the extraction of argumentative techniques from text.