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operate on someone
to perform a surgical operation on someone. They decided not to operate on her. She wasn't operated on after all.
operate on something
1. to work on something; to work with the insides of something. (As a surgeon might operate.) He tried to operate on his watch and ruined it. Todd operated on the door lock and fixed it.
2. to function or conduct business on a certain principle or assumption. The company has always operated on the theory that the customer is always right. Sam operates on the assumption that everyone is out to get him.