Judge Frans Kgomo postponed the matter to November 17 during Agliotti's brief appearance on Friday.
The argument was meant to be heard on Friday but Agliotti's defence team failed to hand in their heads of argument to the State on time.
This was due to financial constraints which Agliotti experienced. This had since been ironed out and the papers were filed on Friday.
The State has until next Friday to respond to them and prepare their own heads of argument.
The matter will then again come before the court.
Agliotti's defence team led by Advocate Laurance Hodes SC applied for a discharge of all four charges at the convicted drug trafficker's last appearance on October 26.
The State is opposing the application.
Four murder charges
It closed its case after calling fewer than 10 witnesses at the end of last month. A key witness, Kebble's security boss Clinton Nassif, was questioned for days by Hodes. He meticulously pointed out contradictions in Nassif's testimony to the court, compared to his signed statements.
Agliotti was arrested in 2006 for the 2005 shooting of mining magnate Brett Kebble. He has been out on bail ever since - but spent a large amount of time under house arrest. This part of his bail conditions was lifted in August 2010.
He is facing four charges, one of murder, one charge of attempted murder and two counts of conspiracy to commit murder.
The murder charge relates to the 2005 shooting of mining magnate Brett Kebble in Melrose.
Agliotti is further accused of conspiring to kill Alan Gray auditor Stephen Mildenhall, Jean Daniel Nortier, Dr Mark Bristow and Mark Wellesley Woods.
The attempted murder charge relates to the shooting of Mildenhall in Cape Town in August 2005.