A modified fractal spiral forked plate (MFSFP) is proposed to generate three tailorable coplanar optical vortices at multiple focal planes, which consist of two off-axis vortices and one axial vortex. The axial vortex and one low-intensity off-axis vortex can have equal intensity by designing an appropriate spiral-like filter. In addition, the MFSFP has self-similar axial and off-axis optical vortices. Moreover, the tailorable topological charges of two off-axis vortices are related to those of the fractal spiral zone plate (FSZP) and forked grating and the topological charge of the axial vortex is equal to that of the FSZP. In the experiments, based on the interferometric measurement method, the differences between fingers of forked fingers are used to prove the above topological charge transformation rule. The method of constructing the MFSFP is illustrated. The MFSFP is applicable to rotate particles at multiple positions of the different planes simultaneously, increase optical communication capacities and produce multiple images simultaneously. © 2021 IOP Publishing Ltd.