An amicus curiae brief, asking the U.S. Supreme Court to hear Utah Republican Party v Cox, has been filed by some minor parties, along with other groups, including the Coalition for Free & Open Elections (COFOE). The brief is also joined by the Utah Native American caucus (which contains eleven legislators from both major parties), and the Idaho Republican Party.
The minor parties who signed the brief are the Green Party, the Constitution Party, and the American Independent Party. Also these state Libertarian Parties joined: California, Georgia, Louisiana, Michigan, New Mexico, and Oklahoma. Here is the brief.
Another amicus has been filed by Judicial Watch. See it here.
Yet another amicus has been filed by Eagle Forum Legal Defense Fund. See it here.
The next event in this case will be when the U.S. Supreme Court sets a conference date. Also, the Court may then ask the state to respond.