The decays B-s(0) -> J/psi pi(+)pi-K+K- are studied using a data set corresponding to an integrated luminosity of 9 fb(-1), collected with the LHCb detector in proton-proton collisions at centre-of-mass energies of 7, 8 and 13TeV. The decays B-s(0) -> J/psi K*(K) over bar 0 and B-s(0) -> chi(c1)(3872)K+K-, where the K+K- pair does not originate from a phi meson, are observed for the first time. Precise measurements of the ratios of branching fractions between intermediate chi(c1)(3872)phi, J/psi K0 (K) over bar *0, psi(2S)phi and chi(c1)(3872)K+K- states are reported. A structure, denoted as X(4740), is observed in the J/psi phi mass spectrum and, assuming a Breit-Wigner parameterisation, its mass and width are determined to be

m(X(4740)) = 4741 +/- 6 +/- 6 MeV/c(2),

Gamma(X(4740)) = 53 +/- 15 +/- 11MeV,

where the first uncertainty is statistical and the second is systematic. In addition, the most precise single measurement of the mass of the B-s(0) meson is performed and gives a value of

m(Bs)(0) = 5366.98 +/- 0.07 +/- 0.13MeV/c(2).