Rotation is a mathematical concept, not a physical one.

In 4d, an object can rotate about two axes at once. Say the 4 coordinates are w x y z. The w and x coordinates can do the usual rotation, while the y and z coordinates rotate together, perhaps at a different rate. Or instead of 4 real coordinates, take 2 complex coordinates a and b, and have them evolve by (a,b) → (exp(i.r.t).a, exp(i.s.t).b), where t is the time and r and s are speeds.