There is a wealth of material that we do in class but which has no obvious home in the syllabus; exercises that are not precisely conditioning, nor do they belong to a specific historical system.
One such is the stepping drill, which shares a some DNA with push-hands, but is not, and some with wrestling, but is not. The idea is that the two players face off and try to make the other move a foot. Once that is going nicely, each player may be allowed a single step, to use in attack or defence; the second step loses the match. This is suposed to be done with minimum physical force, and in a spirit of friendly competition.
There are several arts that are clearly not historical, european or even swordsmanship, which nonetheless may be learned at the school, usually through individual tuition. For example, the Cheng Man-Ching Yang-style short T'ai Chi Chuan form.