The two-way balanced one-level rotation design, $r_1^m-r_2^{m-1}$, and the three-way balanced multi-level rotation design, $r_1^m(iota)-r_1^{m-1}$, were discussed (Park et al., 2001, 2003). Although these rotation designs enjoy balancing properties, they have a restriction of $r_2=c{cdot}r_1$ (c should be a integer value) which interferes with applying these designs freely to various situations. To overcome this difficulty, we extend the $r_1^m(iota)-r_1^{m-1}$ design to new one under the most general rotation system. The new multi-level rotation design also satisfies tree-way balancing which is done on interview time, rotation group and recall time. We present the rule and rotation algorithm which guarantee the three-way balancing. In particular, we specify the necessary condition for the extended three-way balanced multi-level rotation sampling design.