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We study the magnetization process of the $S=1$ Heisenberg model on a two-legladder with farther neighbor spin-exchange interaction. We consider theinteraction that couples up to the next-nearest neighbor rungs and find anexactly solvable regime where the ground states become product states. Thenext-nearest neighbor interaction tends to stabilize magnetization plateaus atmultiples of 1/6. In most of the exactly solvable regime, a singlemagnetization curve shows two series of plateaus with different periodicities.

Multiple magnetization plateaus induced by farther neighbor interaction in an $S = 1$ two-leg Heisenberg spin ladder