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We study the rare B meson decays B{±,0} --> J/\psi\ K^+ K^- K{±,0}, B{±,0} –> J/\psi\ \phi\ K{±,0}, and search for B0 --> J/\psi\ \phi, using 469 million BBbar events collected at the Upsilon(4S) resonance with the BABAR detector at the PEP-II e+e- asymmetric-energy collider. We present new measurements of branching fractions and a study of the J/\psi\phi mass distribution in search of new charmonium-like states. In addition, we search for the decay B0 --> J/\psi\ \phi, and find no evidence of a signal.

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