Metaphor is a linguistic device in which a concept is expressed by mentioning another. Identifying metaphorical expressions, therefore, requires a non-compositional understanding of semantics. Multiword Expressions (MWEs), on the other hand, are linguistic phenomena with varying degrees of semantic opacity and their identification poses a challenge to computational models. This work is the first attempt at analysing the interplay of metaphor and MWEs processing through the design of a neural architecture whereby classification of metaphors is enhanced by informing the model of the presence of MWEs. To the best of our knowledge, this is the first “MWE-aware” metaphor identification system paving the way for further experiments on the complex interactions of these phenomena. The results and analyses show that this proposed architecture reach state-of-the-art on two different established metaphor datasets.