A two-member bench headed by Justice S J Mukhopadhaya asked the Mistry camp to file within tow days the changes it was seeking in the AoA.
Mistry, who was sacked as Chairman of Tata Sons in 2016 is fighting against the company alleging oppression of minority shareholder.
The bench has also directed Tata Sons and others to file reply within two weeks and posted the matter on December 11, 12 and 13 for next hearing.
During the proceedings, senior advocate C A Sundaram appearing for the Mistry camp said that he was fighting for the future of the company (Tata Sons) and was seeking relief in the interest of the company.
"There are acts of mismanagement and oppression and I am not going open that today. I want to look into future," he said.
Sundaram insisted that he wanted a directorship in Tata Sons as they hold 18 per cent shares of the company.
The Mistry camp had challenged the July 9 order of the Mumbai bench of the NCLT which dismissed their pleas against his removal as Tata Sons chairman, as also the allegations of rampant misconduct on part of Ratan Tata and the company's board.
A special bench of the tribunal had held that the board of directors at Tata Sons was "competent" to remove the executive chairperson of the company.
The NCLT bench had also said that Mistry was ousted as chairman because the Tata Sons' Board and its majority shareholders had "lost confidence in him".
Under the Companies Act 2013, an order of NCLT can be challenged before the National Company Law Appellate Tribunal (NCLAT). Mistry, who was the sixth chairman of Tata Sons, was ousted from the position in October 2016.
He had taken over as the chairman in 2012 after Ratan Tata announced his retirement.
Two months after his removal, Mistry's family-run firms Cyrus Investments Pvt Ltd and Sterling Investments Corp approached the NCLT as minority shareholders, against Tata Sons, Ratan Tata, and some other board members.
Mistry in his pleas primarily argued that his removal was not in accordance with the Companies Act and that there was rampant mismanagement of affairs across Tata Sons.
He also alleged that Tata Trust chairperson Ratan Tata and trustee N Soonawala interfered with the day-to-day operations of the group companies, they acted as shadow directors, and all of the above caused massive revenue loss for the group.