We have searched for the Cabibbo-suppressed decay Λc+→ϕpπ0 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 ϒ(4S) and ϒ(5S) resonances. No significant signal is observed, and we set an upper limit on the branching fraction of B(Λc+→ϕpπ0)<15.3×10−5 at 90% confidence level. The contribution of nonresonant Λc+→K+K−pπ0 decays is found to be consistent with zero, and the corresponding upper limit on its branching fraction is set to be B(Λc+→K+K−pπ0)NR<6.3×10−5 at 90% confidence level. We also search for an intermediate hidden-strangeness pentaquark decay Ps+→ϕp. We see no evidence for this intermediate decay and set an upper limit on the product branching fraction of B(Λc+→Ps+π0)×B(Ps+→ϕp)<8.3×10−5 at 90% confidence level. Finally, we measure the branching fraction for the Cabibbo-favored decay Λc+→K−π+pπ0; the result is B(Λc+→K−π+pπ0)=(4.42±0.05(stat)±0.12(syst)±0.16(norm))%, which is the most precise measurement to date.