We employ a selectively pumped solid-state laser with stimulated Raman scattering and second-harmonic generation to generate frequency-doubled lasing modes (FDLMs) at 588 nm. The FDLMs are transformed by using an external cylindrical mode converter to generate various structured beams with multiple optical vortices. Theoretical analyses clearly reveal the relationship between the mode components in the laser emission and the transverse displacement of the off-center pumping. We further verify that the experimental results for the transformed FDLMs can be numerically reconstructed with a theoretical model. By analyzing the phase structures of the converted beams, it can be demonstrated that the number of vortices rises from 2 to 19 with increasing off-center displacement.