A search for the decays B-s(0) -> mu(+)mu(-)mu(+)mu(-) and B-0 -> mu(+)mu(-)mu(+)mu(-) is performed using data, corresponding to an integrated luminosity of 1.0 fb(-1), collected with the LHCb detector in 2011. The number of candidates observed is consistent with the expected background and, assuming phase-space models of the decays, limits on the branching fractions are set: B(B-s(0) -> mu(+)mu(-)mu(+)mu(-)) <1.6(1.2) x 10(-8) and B(B-0 -> mu(+)mu(-)mu(+)mu(-)) <6.6(5.3) x 10(-9) at 95% (90%) confidence level. In addition, limits are set in the context of a supersymmetric model which allows for the B-(s)(0) meson to decay into a scalar ( S) and pseudoscalar particle (P), where S and P have masses of 2.5 GeV/c and 214.3 MeV/c, respectively, both resonances decay into mu(+)mu(-). The branching fraction limits for these decays are B(B-s(0) -> SP) <1.6(1.2) x 10(-8) and B(B-0 -> SP) <6.3(5.1) x 10(-9) at 95% (90%) confidence level.