Twitter Business Pro customers can suppress tweets from Free, Blue, and Blue Plus accounts for a small fee per tweet. However, if you want to suppress tweets from Gold, Platinum, or Platinum Plus accounts then you'll need to reach out to Twitter Enterprise Sales to discuss your needs further.
Yelp already does this. You can pay to have them hide bad reviews. Or, to put a finer point on it, many small companies that refuse to pay Yelp's protection money find their negative reviews much more visible.
