Former Atomic Kitten singer Kerry Katona, her ex-husband Brian McFadden and footballer Sol Campbell are among the latest names to issue phone-hacking damages claims.
Mr Justice Vos, who will assess compensation in the second round of the civil litigation at an estimated four-week trial now due not before May, was told on Friday that 68 claims were on the register.
Giving an update at London's High Court, Hugh Tomlinson QC said that up to 40 more were likely to be added before the 14 September deadline, with total claims expected to be fewer than 300.
He added that 395 individuals had applied to the Metropolitan Police for disclosure and, of those, 124 had been accepted into the compensation scheme set up by News International, parent company of News Group Newspapers.
The judge, who was conducting the eighth case management conference in the proceedings, said that a three-day hearing starting on 25 September would consider the question of proportionality and the future conduct of the case with regard to further disclosure.
He said: "I am assessing damages. I am not conducting a public inquiry."
The court will also sit on 10 October to consider the publisher's attempt to strike out the claim brought by Mary-Ellen Field, former adviser to model Elle Macpherson, on the basis that no phone interception took place.
There will be another case management conference on 26 October.