on (one's) say-so
With or according to one'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?"
on someone's say-so
on someone's authority; with someone's permission. I can't do it on your say-so. I'll have to get a written request. Bill: I canceled the contract with the A.B.C. Company. Bob: On whose say-so?