We study the decay (B) over bar (0) -> Lambda(+)(c) (p) over bar pi(+) pi(-), reconstructing the Lambda(+)(c) baryon in the pK(-) pi(+) mode, using a data sample of 467 X 10(6) B (B) over bar pairs collected with the BABAR detector at the PEP-II storage rings at SLAC. We measure branching fractions for decays with intermediate Sigma(c) baryons to be B[(B) over bar (0) -> Sigma(c)(2455)(++) (p) over bar (-) pi(-)] = (21.3 +/- 1.0 +/- 1.0 +/- 5.5) X 10(-5), B[(B) over bar (0) -> Sigma(c)(2520)(++) (p) over bar (-) pi(-)] = (11.5 +/- 1.0 +/- 0.5 +/- 3.0) X 10(-5), B[(B) over bar (0) -> Sigma(c)(2455)(0) (p) over bar (-) pi(-)] ¿ (9.1 +/- 0.7 +/- 0.4 +/- 2.4) X 10(-5), and B[(B) over bar (0) -> Sigma(c)(2520)(++) (p) over bar (-) pi(-)] ¿ (2.2 +/- 0.7 +/- 0.1 +/- 0.6) X 10(-5), where the uncertainties are statistical, systematic, and due to the uncertainty on the Lambda(+)(c) -> pK(-) pi(+) branching fraction, respectively. For decays without Sigma(c)(2455) or Sigma(c)(2520) resonances, we measure B[(B) over bar (0) -> Lambda(+)(c) (p) over bar pi(+) pi(-)](non-Sigma c) =(79 +/- 4 +/- 4 +/- 20) X 10(-5). The total branching fraction is determined to be B[(B) over bar (0) -> Lambda(+)(c) (p) over bar pi(+) pi(-)](total) = (123 +/- 5 +/- 7 +/- 32) X 10(-5). We examine multibody mass combinations in the resonant three-particle Sigma(c) final states and in the four-particle Lambda(+)(c) (p) over bar pi(+) pi(-) final state, and observe different characteristics for the (p) over bar pi combination in neutral versus doubly charged Sigma(c) decays.