Verge On is a phrase that means to come close to or approach something. It is often used to describe an action that is almost, but not quite, something else. For example, one might say that someone's behavior verges on rude, meaning that it is close to being rude, but not quite there. The crossword solution for Verge On is BORDER, which is a line that marks the edge of something. This line can be physical, such as a BORDER between two countries, or metaphorical, such as the BORDER between two different ideas.