Dialogue Act tagging with the ISO 24617-2 standard is a difficult task that involves multi-label text classification across a diverse set of labels covering semantic, syntactic and pragmatic aspects of dialogue. The lack of an adequately sized training set annotated with this standard is a major problem when using the standard in practice. In this work we propose a neural architecture to increase classification accuracy, especially on low-frequency fine-grained tags. Our model takes advantage of the hierarchical structure of the ISO taxonomy and utilises syntactic information in the form of Part-Of-Speech and dependency tags, in addition to contextual information from previous turns. We train our architecture on an aggregated corpus of conversations from different domains, which provides a variety of dialogue interactions and linguistic registers. Our approach achieves state-of-the-art tagging results on the DialogBank benchmark data set, providing empirical evidence that this architecture can successfully generalise to different domains.