We study the three-body systems of K¯(*)B(*)B¯(*) by solving the Faddeev equations in the fixed-center approximation, where the light particle K¯(*) interacts with the heavy bound states of BB¯ (B*B¯*) forming the clusters. In terms of the very attractive K¯*B and K¯*B* subsystems, which are constrained by the observed Bs1(5830) and Bs2*(5840) states in experiment, we find two deep bound states, containing the hidden-bottom components, with masses 11002±63 MeV and 11078±57 MeV in the K¯*BB¯ and K¯*B*B¯* systems, respectively. The two corresponding states with higher masses of the above systems are also predicted. In addition, using the constrained two-body amplitudes of K¯B(*) and K¯B¯(*) via the hidden gauge symmetry in the heavy-quark sector, we also find two three-body K¯BB¯ and K¯B*B¯* bound states.