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-A symmetric-energy collider running at or near the Ï'(4S) and Ï'(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.