This study focuses on contextual comparisons that have received much less attention than standard more-than-comparisons. The purpose of this study is to expand the scope of Hohaus’ (2015) framework and enrich it by adding various types of frame phrases that bring different types of degree relations in presuppositions. It is demonstrated that the relations between frame phrases and their main clauses are rule-governed as predicted by Hohaus’ (2015) framework; an asserted degree relation holds only when it satisfies the degree relation in the presupposition brought by its frame phrase(s). Relevant data will be provided in English and Japanese.