Rare B decays into states containing a J/psi meson and a meson with s(s)over-bar quark content

We report a study of the B meson decays, B+-->J/psiphiK(+), B-0-->J/psiphiK(S)(0), B-0-->J/psiphi, B-0-->J/psieta, and B-0-->J/psieta' using 56x10(6) B (B) over bar events collected at the Y(4S) resonance with the BABAR detector at the PEP-II e(+)e(-) asymmetric-energy storage ring. We measure the branching fractions B(B+-->J/psiphiK(+))=(4.4+/-1.4(stat)+/-0.5(syst))x10(-5) and B(B-0-->J/psiphiK(S)(0))=(5.1+/-1.9(stat)+/-0.5(syst))x10(-5), and set upper limits at 90% confidence level for the branching fractions B(B-0-->J/psiphi)<9.2x10(-6), B(B-0-->J/psieta)<2.7x10(-5), and B(B-0-->J/psieta('))<6.3x10(-5).