They claim senior editors and executives at MGN knew about and approved of the wrongdoing.
MGN, owned by Reach (RCH.L), is fighting the lawsuit, saying there was no evidence for the accusations.
The claimants want the judge to rule on whether Morgan and other senior figures were involved in unlawful acts.
MGN's failure to call Morgan and other journalists "leaves enormous holes, we say fatal holes, in the defendant's case," he said.
At the start of the trial in May, MGN did admit on one occasion a private investigator had been engaged to unlawfully gather evidence about him.
Persons:
Prince Harry's, Piers Morgan, David Sherborne, MGN, Morgan, Prince Harry ", Sherborne, Mr Morgan, Duke of Sussex, Duke, Sussex, Michael Holden, Ed Osmond
Organizations:
Group, Daily, Sunday, MGN, Reach, London's, Thomson
Locations:
British