verge

on the verge (of doing something) and on the verge of something

at the very beginning of doing something; just about to do something. Bill was on the verge of leaving town when he found a job. Susan was on the verge of laughter, so she left the lecture hall.

verge (up)on something

to be almost identical to something; to be similar to or almost the same as something. (Upon is formal and less commonly used than on.) Your actions verge upon mutiny. What you said verges on an insult.

verge into something

to change gradually into something. The reds verged into a violet color that seemed to glow. The cool morning verged imperceptibly into a steamy midday.

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on the verge of doing something

almost doing or experiencing something He was on the verge of making a comment but stopped, realizing it would be a mistake.