Oler is accused of polygamy for allegedly having four wives.
None of the allegations have been proven in court and the case is being heard by a judge.
Blackmore's lawyer, Blair Suffredine, told the court on Tuesday that the polygamy charges involve separate and different allegations, with no factual overlap.
If tried together, evidence against Oler could be prejudicial against Blackmore and vice versa, he said.
"The sins of one are being alleged against the other," Suffredine told the court on Tuesday.
Peter Wilson, a special prosecutor appointed by the provincial government, argued that expert evidence was going to be called from witnesses in the United States and that it wouldn't make sense to have them come to Canada again for a second trial.
"It's undesirable and contrary to the interests of justice to run the same trial twice," said Wilson.
Blackmore and Oler are connected to the Fundamentalist Church of Jesus Christ of Latter-Day Saints community of Bountiful in southeastern British Columbia.
The legal history of case goes back to the 1990s when the RCMP began investigating allegations that people in the community were practicing polygamy.
Three special prosecutors have been appointed to assess charges since 2007, and a constitutional reference case was launched after charges were thrown out in 2009. A B.C. Supreme Court judge later ruled that the polygamy charges were constitutionally valid.
Wilson was the third special prosecutor hired and in August 2014, Blackmore and Oler were charged with polygamy.