The High Court has been told businessman Denis O'Brien continues to suffer harm as a result of alleged defamation by the Red Flag Consulting firm.
His lawyers have asked the court to hear an application concerning discovery of documents as soon as possible.
The documents relate to Mr O'Brien's action against Red Flag and are "central" to the case, according to his barrister Martin Hayden.
The court also may have to decide a dispute between the sides over access to the Dropbox account of a Red Flag employee, he added.
Mr Justice Colm MacEochaidh adjourned the case to 31 May and said he will determine whether or not the matter is urgent.
He said there were hundreds of defamation actions before the courts and "screaming urgency" would have to be shown to allow this case get priority over others.
Mr Hayden said the urgency arises because the harm to Mr O'Brien is continuing.
The judge said many plaintiffs in defamation actions make similar complaints.
He said he would decide later if there was any element to justify this case getting priority over others.
Mr O'Brien brought the case against Red Flag last October.
He claims a USB computer memory stick sent anonymously to his Dublin office contained a dossier of defamatory material.
He claims Red Flag and some of its executives were engaged in a conspiracy to defame him.
The material mainly involves media stories about Mr O'Brien and his business interests.
