Sure, you can take classes in the summer and you might have to be creative to maintain necessary credit levels to satisfy eligibility requirements. There are going to be some classes that are required to be taken in a certain order or as foundation for other work. In law school, for example, the first year curiculum is set so that all students take a set of core classes, usually without any electives. These courses build fundamental concepts that carry over to later work and are largely independent of one another. It would be possible to to take those courses over two years instead of one as would a regular full-time law student. Any credit shortcomings could be met by independent study, research at the direction of a professor, etc.
A student-athlete wanting to pursue this type of graduate program would require the cooperation of the school or program they wanted to be in. It would absolutely not be a "typical" post-graduate course load or course progression, but that wasn't the initial question. The original take by GoldenRodents was that it could not be done. I still believe that it could, it would not be the "typical" student experience, but it could be done.