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We have searched for the Cabibbo-suppressed decay Lambda(+)(c) -> pi p(0) in e(+) e(-) collisions using a data sample corresponding to an integrated luminosity of 915 fb(-1). The data were collected by the Belle experiment at the KEKB e(+) e(-) asymmetric-energy collider running at or near the (4S) and (5S) resonances. No significant signal is observed, and we set an upper limit on the branching fraction of B(Lambda(+)(c) -> phi p(0)) < 15.3 x 10(-5) at 90% confidence level. The contribution of nonresonant Lambda(+)(c) -> K+ K- p pi(0) decays is found to be consistent with zero, and the corresponding upper limit on its branching fraction is set to be B(Lambda(+)(c) ->. K+ K- p pi(0))(NR) < 6.3 x 10(-5) at 90% confidence level. We also search for an intermediate hidden-strangeness pentaquark decay P-s(+) -> phi p. We see no evidence for this intermediate decay and set an upper limit on the product branching fraction of B(Lambda(+)(c) -> P-s(+) pi(0)) x B(P-s(+) -> phi p) < 8.3 x 10(-5) at 90% confidence level. Finally, we measure the branching fraction for the Cabibbo-favored decay Lambda(+)(c) -> K- pi(+) p pi(0); the result is B(Lambda(+)(c) -> K- pi(+) p pi(0)) = (4.42 +/- 0.05(stat)+/- 0.12(syst)+/- 0.16(norm))%, which is the most precise measurement to date.