We study the decay Bˉ0→Λc+pˉπ+π−, reconstructing the Λ_{c}^{+} baryon in the pK−π+ mode, using a data sample of 467×106 BBˉ pairs collected with the BaBar detector at the PEP-2 storage rings at SLAC. We measure branching fractions for decays with intermediate Σc baryons to be B[Bˉ0→Σc(2455)++pˉπ−]=(21.3±1.0±1.0±5.5)×10−5, B[Bˉ0→Σc(2520)++pˉπ−]=(11.5±1.0±0.5±3.0)×10−5, B[Bˉ0→Σc(2455)0pˉπ+]=(9.1±0.7±0.4±2.4)×10−5, and B[Bˉ0→Σc(2520)0pˉπ+]=(2.2±0.7±0.1±0.6)×10−5, where the uncertainties are statistical, systematic, and due to the uncertainty on the $Λ_{c}^{+}\rightarrow\proton\Kmπ^{+}$ branching fraction, respectively. For decays without Σc(2455) or Σc(2520) resonances, we measure B[Bˉ0→Λc+pˉπ+π−]non−Σc=(79±4±4±20)×10−5. The total branching fraction is determined to be B[Bˉ0→Λc+pˉπ+π−]total=(123±5±7±32)×10−5. We examine multibody mass combinations in the resonant three-particle Σcpˉπ final states and in the four-particle Λc+pˉπ+π− final state, and observe different characteristics for the pˉπ combination in neutral versus doubly-charged Σc decays.