His proposal to reorganize the troupe raises a host of interesting questions, from how to choose canonical works from modern dance’s past to whether his dancers are suited to other kinds of dance.

Mr. Taylor said that many details were still being worked out, including which contemporary choreographers would be chosen, which past works would be revived and whether those works would all be danced by members of his company, or by others. Asked what choreographers from the past he would be interested in presenting, he mentioned the possibility of Graham, whose company he danced in; Doris Humphrey; and José Limón.

“Those are a few,” he said.

Mr. Taylor has become a fixture in American modern dance, especially in New York, where his company has managed to have regular annual New York seasons for decades, even as it has regularly toured the nation and the world. He danced for seven seasons with the Martha Graham Dance Company, and was a guest artist at New York City Ballet in 1959, where George Balanchine choreographed “Episodes” for him.

Since founding his own troupe in 1954, Mr. Taylor has created 140 dances, including works like “Esplanade,” “Aureole” and “Company B,” and his pieces have been performed by other companies including the Royal Danish Ballet, American Ballet Theater, San Francisco Ballet, Miami City Ballet and Alvin Ailey American Dance Theater. In 2010, Alastair Macaulay wrote in The New York Times, “It is fair to say, though few have done so, that Mr. Taylor’s work became the mainstream of American modern dance more than 35 years ago.”

Mr. Tomlinson said that the first inklings of change would be apparent next month when Tiler Peck and Robert Fairchild, New York City Ballet dancers, perform excerpts from Mr. Taylor’s “Airs” at his company’s gala. Mr. Tomlinson said the changes would be reflected in the 2015 season.

The company has made a number of other plans to celebrate its 60th anniversary. For a special performance on March 11, it is selling all tickets at the Koch Theater for just $6. And at a March 23 performance, several dozen alumni of the company plan to join current members for a performance of Mr. Taylor’s “From Sea to Shining Sea.”