A control system for a work includes an operating device and a controller. The operating device outputs an operation signal indicative of an operation by an operator. The controller is in communication with the operating device. The controller determines a target profile of a terrain to be worked on. The controller generates a command signal to operate the work implement according to the target profile. The controller receives the operation signal from the operating device. The controller determines an operation of the work implement based on the operation signal. The controller corrects the target profile according to the operation by the operator when the operation of the work implement by the operator is performed.