1. make progress with something, arrange something for an earlier time
move forward with a plan/move the appointment forward
To 'move forward with' something means to progress with it. If you chose to move forward, you agree to make the next steps or to continue in the process. To 'move forward' can mean to advance in position or to progress, or it can mean to propel something or someone else forward. If you move an event forward, it means to make something happen at an earlier time than originally agreed.