We present measurements of branching fractions of B0 decays to multibody final states containing protons, based on 232×106 Υ(4S)→BB̅ decays collected with the BABAR detector at the SLAC PEP-II asymmetric-energy B factory. We measure the branching fractions B(B0→D̅ 0pp̅ )=(1.13±0.06±0.08)×10-4, B(B0→D̅ *0pp̅ )=(1.01±0.10±0.09)×10-4, B(B0→D-pp̅ π+)=(3.38±0.14±0.29)×10-4, and B(B0→D*-pp̅ π+)=(4.81±0.22±0.44)×10-4 where the first error is statistical and the second systematic. We present a search for the charmed pentaquark state, Θc(3100) observed by H1 and put limits on the branching fraction B(B0→Θcp̅ π+)×B(Θc→D*-p)<14×10-6 and B(B0→Θcp̅ π+)×B(Θc→D-p)<9×10-6. Upon investigation of the decay structure of the above four B0 decay modes, we see an enhancement at low pp̅ mass and deviations from phase-space in the D̅ p̅ and D̅ p invariant mass spectra.