In this paper, we present a novel approach to multi-word terminology extraction combining a well-known automatic term recognition approach, the C--NC value method, with a contrastive ranking technique, aimed at refining obtained results either by filtering noise due to common words or by discerning between semantically different types of terms within heterogeneous terminologies. Differently from other contrastive methods proposed in the literature that focus on single terms to overcome the multi-word terms' sparsity problem, the proposed contrastive function is able to handle variation in low frequency events by directly operating on pre-selected multi-word terms. This methodology has been tested in two case studies carried out in the History of Art and Legal domains. Evaluation of achieved results showed that the proposed two--stage approach improves significantly multi--word term extraction results. In particular, for what concerns the legal domain it provides an answer to a well-known problem in the semi--automatic construction of legal ontologies, namely that of singling out law terms from terms of the specific domain being regulated.