At issue are about 600 documents the Nazarian family is refusing to hand over to the commission. The Nazarians argue the letters and emails are privileged and should remain confidential.
The commission, which argues the Nazarians have provided no evidence to back their assertion of privilege, has asked Appeal Court Justice Stephen Goudge to rule on the issue.
The public inquiry has been fighting over document access with the Nazarians since last fall. At one point, the matter was headed for Divisional Court until the family relented in March and turned over about 85,000 emails.
The Nazarians later claimed blanket solicitor-client or litigation privilege over 1,950 of those emails. The commission wants access to 543 of them.
In their application to Goudge this month, the commission states the emails involve third parties and are not subject to secrecy rules.
"We're not seeking any correspondence directly between one of their lawyers and one of the Nazarians," commission lawyer Peter Doody said in an interview Thursday.
Bob Nazarian owned the Algo Centre Mall when it collapsed June 23, 2012, killing two women and injuring several others.
Witnesses at the public inquiry have said Nazarian pressed them to minimize evidence of the mall's crumbling infrastructure, refused to make necessary repairs, and bullied or badgered employees and contractors who raised concerns.
In an affidavit filed Wednesday, Nazarian's lawyer Derek Fulton said he agreed 30 of the documents are not privileged but the rest are.
He also said he was prepared to give those at issue to Goudge to help him make a determination as long as he keeps them confidential.
In addition to the above emails, Nazarian's former lawyer, Paul Mand, is also refusing to turn over 61 documents the inquiry wants. Goudge will rule on those as well.
Mand, of the Toronto firm Mand Rai, claims he does "not feel comfortable" handing over the material he says is privileged.
"On numerous occasions, Mand Rai has tried to obtain the consent of Bob Nazarian for the waiver of privilege," Mand said in an affidavit last week.
"However, our former client has not waived privilege."
Nazarian and his son Levon are scheduled to testify before the inquiry next month. As a result, Goudge set tight deadlines for filing materials on the document dispute.
He gave the parties until the end of Friday to file all relevant materials.
"I will determine the matter before the end of June," Goudge wrote.