beat a path to door
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beat a path to (one's) door
To visit someone in large numbers or a crowd. I'm supposed to try to woo the ex-CEO of that company, but I'm pretty sure every other recruiter in town has beat a path to his door already.
beat a path to someone's door
Fig. [for people] to arrive (at a person's place) in great numbers. (The image is that so many people will wish to come that they will wear down a pathway to the door.) I have a new product so good that everyone will beat a path to my door. If you really become famous, people will beat a path to your door.