Twenty more gymnasts have alleged they have suffered physical and psychological abuse after a group of 17 launched a legal case against British Gymnastics last month.
The group has complained about the conduct of coaches and people employed by UK clubs over the past 40 years.
A spokesperson for the gymnasts says the number who have already come forward is the "tip of the iceberg".
An investigation into allegations of abuse at British Gymnastics is ongoing.
Law firm Hausfeld, which is representing the group, asked British Gymnastics to provide a response this week to a letter before action - the process to inform a potential defendant of a claim - which it issued last month.
The firm says it will pursue the matter through the courts if British Gymnastics has not provided a substantive response by 19 June.
Hausfeld said British Gymnastics had asked for an extension until 19 December.
The group involved in the action felt the request from the governing body was unacceptable and was putting "current gymnasts at risk of similar serious harms".
British Gymnastics has not commented further.
After the legal case was launched last month, the governing body said: "It would not be appropriate or fair to all parties for us to make any comment until we have had the opportunity for it to be fully considered."