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