The effects of chemical doping by P, Yb, Co, and Cu, and hydrostatic pressure on CaFe4As3, were studied on single-crystalline samples. While the former two dopants substitute the nonmagnetic ions, the latter two partially occupy the Fe sites within the magnetic sublattice. The incommensurate spin density wave (IC-SDW) ordering at TN∼ 88 K in CaFe4As3 changes only by up to ∼40% with doping and applied pressure. Thus the IC-SDW state appears more robust than in the layered Fe pnictides. The commensurate SDW (C-SDW) state below T2∼ 26 K is suppressed in the Co-doped series, while it moves up in temperature in the P-, Yb-, and Cu-doped compounds. A new magnetic phase transition is observed at an intermediate temperature T3 in Ca(Fe1−xCox)4As3. Resistivity and magnetization measurements on CaFe4As3 were performed under hydrostatic pressure up to 5 GPa, showing a systematic decrease of TN and a domelike phase boundary at T2 up to pc∼ 2.10 GPa. At higher pressures, a possible structural phase transition occurs, marked by a slowly increasing transition temperature. A phase diagram is shown to compare the effects of chemical doping and pressure.