A search for charge-parity (CP) violation in Cabibbo-suppressed D-s(+) -> K-S(0)pi(+), D+ -> (KSK+)-K-0, and D+ -> phi pi(+) decays is reported using proton-proton collision data, corresponding to an integrated luminosity of 3.8 fb(-1), collected at a center-of-mass energy of 13 TeV with the LHCb detector. High-yield samples of kinematically and topologically similar Cabibbo-favored D-(s())+ decays are analyzed to subtract nuisance asymmetries due to production and detection effects, including those induced by CP violation in the neutral kaon system. The results are A(CP)(D-s(+) -> K-S(0)pi(+)) = (1.3 +/- 1.9 +/- 0.5) x 10(-3), A(CP)(D+ -> (KSK+)-K-0) = (-0.09 +/- 0.65 +/- 0.48) x 10(-3), A(CP)(D+ -> phi pi(+)) = (0.05 +/- 0.42 +/- 0.29) x 10(-3), where the first uncertainties are statistical and the second systematic. They are the most precise measurements of these quantities to date, and are consistent with CP symmetry. A combination with previous LHCb measurements, based on data collected at 7 and 8 TeV, is also reported.