Unfortunately, you could only sue the people who made the defamatory statements about your company rather than Yelp, as Yelp isn’t legally responsible for the content that is posted there. The people who are posting it are responsible for making false and damaging statements. (Yelp has no way of knowing whether it is true or false).
That said, they definitely have negligent business practices for them to post comments about the previous business in the same place as your business solely because they share the same address, thereby damaging your business’ reputation. Although you cannot sue for defamation
(which would also be very costly and unlikely to succeed), you can file a complaint against yelp with the Better Business Bureau
They currently have an A + rating, and wouldn’t want that to lower, so they will definitely work with you to resolve your complaint, including taking down the content that exists prior to when your business existed and is actually about another business and not yours. The response time is nearly immediate and you can work on getting a resolution within a few days or weeks as opposed to the months or years too that a defamation case would possibly take.
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