Self-Organized Laser Functionalization (SOLF) is a cutting-edge manufacturing technology that permanently modifies material properties by creating self-organized quasi-periodic micro- and nano-scale structures. SOLF can produce surfaces with diverse structures tailored for applications such as heat transfer enhancement, corrosion resistance, broadband light absorption, and super-wicking capillary channels. These structures and their properties can be precisely controlled by tuning laser processing parameters, with laser fluence and pulse count being key factors in achieving desired surface topographies. However, while the influence of fluence and pulse count is well-studied, the roles of pulse overlap (PO) and raster line overlap (LO) remain relatively unexplored. In this work, we systematically decouple the effects of PO (ranging from 99.8% to -42.8%) and LO (0% to 99.8%) on crystalline silicon while maintaining constant pulse counts across a range of fluences. For the first time, we explore extreme PO and LO conditions, including PO below -42.8% and LO exceeding 99.8%, as well as negative overlap regimes where pulses are spaced farther apart. Investigating negative overlaps may reveal novel structures, as widely spaced pulses in the raster line act more independently, producing isolated features rather than continuous patterns. Conversely, high LO induces continuous transverse structures perpendicular to the scanning direction. By correlating LO and PO with surface and subsurface structure formation, we provide fundamental insights into micro- and nano-structuring via SOLF under these extreme processing conditions.