One way in which metaphor and metonymy can interact and thus one kind of the more general phenomenon known as metaphtonymy.

In this form of interaction, a metaphor is grounded in a metonymic relationship. For example, the expression close-lipped can mean 'silent', which follows from metonymy: when one has one's lips closed, one is (usually) silent, therefore to describe someone as close-lipped can stand metonymically for silence. However, close-lipped can also mean 'speaking but giving little away'. This interpretation is metaphoric, because we understand the absence of meaningful information in terms of silence. The metaphoric interpretation has a metonymic basis, in that it is only because being closed-lipped can stand for silence that the metaphoric reading is possible: thus metaphor from metonymy.