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 Standing Step 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.
Another is the rope exercise, in which a rope tied around the hips is used to teach students the sense of moving from the hip.
And we have "the stick exercise", in which while the students are practising their footwork (and solo drill will do), the instructor wanders around swinging a stick at the students. They have to get out of the way without flinching, and get behind him and tap him gently on the back. The idea is to practise moving fluently and easily, and to maintain situational awareness even when doing mechanical drills. The vigour of the stick should be proportional to the experience of the student. A touch of the stick costs the student three push-ups.
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.