We study the three-body systems ofK ( * ) B ( * )B( * ) by solving the Faddeev equations in the fixed-center approximation, where the light particleK ( * ) interacts with the heavy bound states of BB (B * B * ) forming the clusters. In terms of the very attractiveK * B andK * 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±63 MeV and 11078±57 MeV in theK * BB andK * 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 ofKB ( * ) andKB ( * ) via the hidden gauge symmetry in the heavy-quark sector, we also find two three-bodyKBB andKB * B * bound states. With the development of experiments, a large number of hadronic states have been reported [1], which provides an ideal playground to deepen our understanding of the nonperturbative quantum chromodynamics (QCD). The interpretation of hadronic states is one of the most important issues in hadronic physics (see Refs. [2-7] for reviews), particularly for the exotic states which cannot be easily collected as qq or qqq states, e.g. the so-called XY Z states. Recently, the exotic hadrons with the open/hidden heavy quark components, such as Z c (3900) [8, 9], Z b (10510) and Z b (10560) [10], P c (4380) and P c (4450) [11], have been reported and attracted great attention from the experimental and theoretical physicists. Most of the heavy flavor meson resonances can be interpreted as the tetraquarks [12-14] and/or the meson-meson molecules [2, 15-21]. Besides, several heavy flavor mesons have been predicted in the three-body systems, like ρD ( * )D( * ) [22, 23], ρB * B * [24], KDD [25], KDD * [26, 27],KBB * [26],KBThe standard method to study three-body systems refers to the Faddeev equations [32]. Since it is very difficult to solve exactly, one usually introduces some reasonable approximations of the Faddeev equations, such as the use of separable potentials and energy-independent kernels, the widely-used Alt-Grassberger-Sandras approach [33]. Recently, a different approach to solve the Faddeev equations was proposed to study the three-hadron systems [34][35][36], which relies on the on-shell two-body scattering amplitudes. In addition, another approximation of the Faddeev equations, which is the so-called fixed-center approximation (FCA), has been employed in the studies ofKd interaction at low energies [37][38][39][40]. In Refs. [41,42], it is shown that the FCA is a rather good approximation, especially for the system with one light particle and one heavy cluster formed by the other two particles. Nowadays, the FCA has been applied in many problems [22-24, 27, 30, 31, 43-60] and is accepted as a reasonable tool in the study of bound systems: such as the systems with three mesons: φKK [47], ηKK and η ′ KK [49], ρKK [50], ρDD [23], ρD * D * [22], ρB * B * [24], η ′ KK [51], πKK * [52], DKK and DKK [53],...