Unlike traditional optical vortex (OV), helico-conical optical beams (HCOBs) carry orbital angular momentum (OAM) related to the beam's radius and exhibit a helical intensity pattern, drawing widespread attention in fields such as optical communication and optical tweezers. In this study, we introduce two independent power-exponents into the HCOB configuration and employ spin-isolated geometric phase metasurfaces to simultaneously generate dual bi-power-exponent helico-conical beams (BPE-HCBs). This innovative approach allows unprecedented control over the beams' shape and intensity using only simple linearly polarized (LP) incident light, facilitating the transformation from dual helical structures to multi-ring hollow beams and vector vortex beams (VVBs) patterns. Our research not only simplifies the design process of metasurfaces but also demonstrates their significant capabilities in generating and manipulating complex OAM beam patterns, paving the way for innovative designs in integrated optical systems.