verge

(noun) a region marking a boundary. Synonyms: brink, threshold.

(noun) the limit beyond which something happens or changes. Synonyms: brink. Examples: "On the verge of tears." "On the brink of bankruptcy."

(noun) a ceremonial or emblematic staff. Synonyms: scepter, sceptre, wand.

(noun) a grass border along a road.

(verb) border on; come close to. Example: "His behavior verges on the criminal."