Avi Yemini wants to sue the user known as PRGuy for defamation, but can't without knowing the user's identity.
He has taken action in the Federal Court, attempting to force Twitter to hand over identifying details which the social media giant says it won't hand over without a court order.
Twitter is challenging Mr Yemini's application over jurisdictional issues which the company's lawyer Premala Thiagarajan on Tuesday argued should be dealt with before any further matters are considered.
She estimated those arguments could take a full day and include evidence from expert witnesses.
But Shannon Jenkins, for Mr Yemini, said his application for preliminary discovery of information from Twitter should be heard at the same time to save multiple court dates.
He questioned the need for expert witnesses, suggesting jurisdictional issues were straightforward and would take no more than half a day.
Justice Debbie Mortimer wasn't sure she shared Mr Jenkins' confidence and suggested the lawyers talk through the issues together before setting a court date.
She also revealed she would be unable to hear the case until September at the earliest.
Other court dates aren't available until early November.
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