Not in a way that matters
My understanding is that the DMCA does have restrictions against abuse, but they are written in such a way that they don't apply to this problem. The model of the DMCA is to let the copyright holders issue complaints quickly and easily and let those targeted by the complaints respond if they want. You can get in trouble very easily for issuing a take down when you don't represent the copyright holder or give the wrong information on what to take down. But to get somebody for targeting something that isn't infringing, you have to prove they knew the material was not infringing when they issued the take down. The copyright holder gets all of the benefit of the doubt.