on somebody's say-so

on (one's) say-so

With or according to someone's authorization or permission. Although I'm the manager of this department, I can only make changes to the way things run on the general manager's say-so. A: "We're going to start transferring the funds into the new account." B: "On whose say-so?"
See also: on

on somebody’s ˈsay-so

based on a statement that somebody makes without giving any proof: He hired and fired people on his partner’s say-so.
See also: on