  We study the three-body systems of $\bar{K}^{(*)}B^{(*)}\bar{B}^{(*)}$ by
solving the Faddeev equations in the fixed-center approximation, where the
light particle $\bar{K}^{(*)}$ interacts with the heavy bound states of
$B\bar{B}$ ($B^*\bar{B}^*$) forming the clusters. In terms of the very
attractive $\bar{K}^*B$ and $\bar{K}^*B^*$ subsystems, which are constrained by
the observed $B_{s1}(5830)$ and $B_{s2}^*(5840)$ states in experiment, we find
two deep bound states, containing the hidden-bottom components, with masses
$11002\pm 63$ MeV and $11078\pm 57$ MeV in the $\bar{K}^*B\bar{B}$ and
$\bar{K}^*B^*\bar{B}^*$ 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 $\bar{K}B^{(*)}$ and
$\bar{K}\bar{B}^{(*)}$ via the hidden gauge symmetry in the heavy-quark sector,
we also find two three-body $\bar{K}B\bar{B}$ and $\bar{K}B^{*}\bar{B}^*$ bound
states.
