He is one of the great draftsmen of the impressionist era, acclaimed for strongly structured compositions and a masterful use of line. But when Edgar Degas discovered the printmaking technique known as monotype, everything changed.

As a major exhibition due to open at the Museum of Modern Art next spring reveals, he became much looser and more improvisational in his working methods. He regularly mixed printmaking with other media, like pastel. And he expanded past the subjects for which he is best known—dancers and scenes...