Wiktionary
vb. (context transitive idiomatic English) To approach or come close to something; to border or be on the edge of something.
Usage examples of "verge on".
Life's great tensions verge on chaos and the madness of exaltation.
Everything else was aquamarine, a sunken meadow, fresh scent of vespertine breezes, sounds he'd never heard before, how the wind made forests seem to verge on bursting and where a hidden stream failed in sand, all tempered within by vanishing light, the abundant sundown blush that made this oceanic hour whisper to the senses.
Hazel reached the hedge, crossed a narrow turf verge on the other side and found himself looking straight down a long, shadowy aisle between two rows of beans.
He identified the animal just as it was disappearing into the overgrown verge on the opposite side of the road.
But with the grassy verge on either side of the road jammed with cheering, waving commoners, he could hardly repress his excitement.