As far as I am aware, there is not. Generally when you heavily hole dope these materials, you are in a fermi liquid regime. So this means the electrons are essentially a non-interacting fermi gas. The idea would be that whatever the strong correlations were that gave rise to superconductivity in the cuprates have now become too weak to form a superconducting condensate. But one ask if there could be some other interaction to create pairing at those dopings. So your original question is a good one.