We report a search for the decays B(0) -> K*(0)(K) over bar*(0) and B(0) -> K*(0)K*(0) . We also measure other charmless decay modes with K(+) pi(-)K(-)pi(+) and K(+)pi(-)K(+)pi(-) final states. The results are obtained from a data sample containing 657 x 10(6) B (B) over bar pairs collected with the Belle detector at the KEKB asymmetric- energy e(+)e(-) collider. We set upper limits on the branching fractions for B(0) -> K*(0)(K) over bar*(0) and B(0) -> K*(0)K*(0) of 0: 81 x 10(-6) and 0.20 x 10(-6), respectively, at the 90% confidence level.