Verge upon is an idiomatic expression that means something is about to happen or reach a certain point. The word 'border' is a perfect synonym for verge upon. The expression has the same connotation and usage as 'edge toward,' 'approach,' and 'come close to.' Other synonyms for the phrase include 'border on,' 'lead to,' 'hint at,' and 'nearly.' These words suggest the idea of nearness, proximity, or even the inevitability of an event happening. It is important to note that the context surrounding the usage of verge upon will help determine which synonym to use in each specific situation.