The board of the National Theatre yesterday expanded a team of members to work out the theatre's differences with the Shubert Organization, the New York-based production company that books the theater, and voted to foster a "new spirit of cooperation," according to one member.

The chairman of the National's board, Maurice B. Tobin, and the Shubert Organization have been battling over the question of how much income the theater should get from its arrangement with the production company. The theater is run by a nonprofit corportion that contracts with the Shuberts for show. The board members added to the negotiating team are vice president Harry Teter Jr. and treasurer John B. Adams Jr.; and according to one board member, the team has been instructed to work out the problems rather than to "deliver ultimatums."

The first meeting between the new team and the Shubert Organization is scheduled to take place next week.

A spokesman for the theater said a statement on the board meeting would be issued next week.

The theater is scheduled to close for 4 1/2 months after tomorrow's final performance of "The Pirates of Penzance," during which time major renovations to the aging structure are supposed to be made. Board members were assured yesterday that construction would begin shortly. Tobin has announced the theater will reopen Sept. 15.

At the previous board meeting, said one member, the sentiment had been to cancel the contract, with the Shuberts. This time the feeling was the opposite, he said.