The relevance of automatically identifying rhetorical moves in scientific texts has been widely acknowledged in the literature. This study focuses on abstracts of standard research papers written in English and aims to tackle a fundamental limitation of current machine-learning classifiers: they are mono-labeled, that is, a sentence can only be assigned one single label. However, such approach does not adequately reflect actual language use since a move can be realized by a clause, a sentence, or even several sentences. Here, we present MAZEA (Multi-label Argumentative Zoning for English Abstracts), a multi-label classifier which automatically identifies rhetorical moves in abstracts but allows for a given sentence to be assigned as many labels as appropriate. We have resorted to various other NLP tools and used two large training corpora: (i) one corpus consists of 645 abstracts from physical sciences and engineering (PE) and (ii) the other corpus is made up of 690 from life and health sciences (LH). This paper presents our preliminary results and also discusses the various challenges involved in multi-label tagging and works towards satisfactory solutions. In addition, we also make our two training corpora publicly available so that they may serve as benchmark for this new task.