Hi, yes, this is entirely possible. But the strategy can be time consuming and expensive.
I would think about getting positive articles about your store published on the same news and local sites to out rank the negative articles.
Failing that, find out other high authority local and news sties you can publish feature articles on and try to get those to outrank the negative articles. It's a process that will take months, but it comes down to building backlinks on more relevant articles and publish better content (i.e. longer more informative content) on websites that show you in a positive light.