Representing predicates in terms of their argument distribution is common practice in NLP. Multi-word predicates (MWPs) in this context are often either disregarded or considered as fixed expressions. The latter treatment is unsatisfactory in two ways: (1) identifying MWPs is notoriously difficult, (2) MWPs show varying degrees of compositionality and could benefit from taking into account the identity of their component parts. We propose a novel approach that integrates the distributional representation of multiple sub-sets of the MWP's words. We assume a latent distribution over sub-sets of the MWP, and estimate it relative to a downstream prediction task. Focusing on the supervised identification of lexical inference relations, we compare against state-of-the-art baselines that consider a single sub-set of an MWP, obtaining substantial improvements. To our knowledge, this is the first work to address lexical relations between MWPs of varying degrees of compositionality within distributional semantics.