In this chapter, I analyse the contribution made by have to the meanings expressed in sentences with a (central) modal verb followed by a perfect infinitive. Four meanings are discussed: (a) have as a marker that locates the possibility or necessity in the past; (b) have as a marker that establishes a relation of anteriority between the modal meaning (of possibility or necessity) and the situation referred to, (c) have as a marker of counterfactual meaning, (d) have as a marker of actualization. In the first part of the chapter an empirical overview is given. Drawing on the discussion in Chap. 2, I then address the question of how the role of the context should be captured, more specifically, whether it is saturation or free pragmatic enrichment that plays a role in bringing about the different meanings of non-finite have when it combines with a modal.