Structured Illumination Microscopy (SIM) is gaining increasing attention in the field of bioimaging for its capability to strike a balance between high spatial resolution and fast imaging speed. However, adopting SIM in high-dimensional imaging faces various challenges, including aberrations, limited color channel availability and the long acquisition time for a whole high-dimensional data cube. Here, a novel snapshot multi-dimensional structured illu- mination microscopy (SIM) imaging system is devised to addresses these issues and achieves the following: (1) Aberration-corrected super-Resolution Imaging: We introduce a hybrid adaptive optics system, TACO, correcting both illumination and excitation aberrations. This results in high-quality SIM super-resolution imaging even in highly aberrative environments. (2) Scalable multi-color Imaging: A dispersion compensation grating module was designed to correct the divergence of different excitation wavelength beams, enabling effortless increase in the number of color channels with minimal realignment. (3) Multi-scan 3D Imaging: Simultaneous multiplane imaging is achieved through a specialized multi-plane beam split- ter. A deformable mirror facilitates rapid z-scan and aberration correction, ensuring fast, aberration-free volumetric imaging. (4) Virtual multi-channel imaging: Our system adapts a convolutional neural network model with a novel architecture for automated decomposition of multiple cellular structures in a single channel. (5) Single-Shot SIM super-resolution re- construction: a novel SIM reconstruction algorithm is developed to enable super-resolution reconstruction from one snapshot by encoding multiple image frames through compressive patterns. The presented SIM system’s capabilities have been rigorously validated through experimental imaging or computational simulation. These innovations significantly broaden the application of SIM in complex high-dimensional data acquisition tasks.