SALT LAKE CITY -- Reality TV polygamist Kody Brown and his wives have been given more time to pursue an appeal to the nation's top court in their lawsuit against the state of Utah over polygamy.

In a filing with the 10th U.S. Circuit Court of Appeals in Denver, U.S. Supreme Court Justice Sonia Sotomayor granted the Brown family's request for additional time to file a petition for certiorari. They have until Sept. 10.

Brown family attorney Jonathan Turley had previously told FOX 13 he would be taking their case to the U.S. Supreme Court after the 10th Circuit ruled against them.

Brown and his four wives, Meri, Christine, Janelle and Robyn, sued Utah in 2012 over its historic ban on plural marriage. The family was the subject of a bigamy investigation by police in Lehi shortly after their TV series, "Sister Wives" began airing. The Browns said the state's anti-polygamy laws infringe on their rights to privacy and religious freedom. In 2014, about a week before another federal judge struck down Utah's same-sex marriage ban, U.S. District Court Judge Clark Waddoups struck down a portion of Utah's polygamy ban and made it no longer a crime to cohabitate with multiple people and purport to be married.

The state appealed and the 10th U.S. Circuit Court of Appeals reversed it earlier this year. The U.S. Supreme Court has not considered a polygamy case in more than 100 years.

There are an estimated 30,000 people who believe in fundamentalist Mormonism, the belief system that includes the practice of polygamy. The Utah Attorney General's Office has repeatedly insisted it will not prosecute polygamy alone, but in concert with crimes like underage "marriages," abuse and fraud.

Recently, members of Utah's polygamous communities have begun pushing the state legislature to consider decriminalization of plural marriage.