Preferences between different alternatives (products, decisions, agreements etc.) are often based on multiple criteria. Qualitative Preference Systems (QPS) is a formal framework for the representation of qualitative multi-criteria preferences in which a criterion's preference is defined based on the values of attributes or by combining multiple subcriteria in a cardinality-based or lexicographic way. In this paper we present a language and reasoning mechanism to represent and reason about such qualitative multi-criteria preferences. We take an argumentation-based approach and show that the presented argumentation framework correctly models a QPS. Then we extend this argumentation framework in such a way that it can derive missing information from background knowledge, which makes it more flexible in case of incomplete specifications.