edge in (on)
edge in (on) {v. phr.}
1. To gradually approach an individual or a group with the intent of taking over or wielding power.
Jack was edging in on the firm of Smith and Brown and after half a year actually became its vice president.
2. To approach for capture (said of a group).
The hunters were edging in on the wounded leopard.
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Source: A Dictionary of American Idioms