The idea under discussion with Spotify, Apple Music and Amazon Music would operate much like the one laid out by the Digital Millennium Copyright Act but would cite violations of rights of publicity, rather than copyright, according to sources at all three majors. Unlike the DMCA, however, this arrangement appears to be voluntary. Citing rights of publicity can be more complicated than copyright, because they are matters of state law in the U.S., backed by limited legal precedent.
Source: Major Labels to Send ‘Takedown Notices’ to Streaming Services for AI Soundalikes