In the pursuit of reliable energy storage solutions, the significance of engineering electrodes cannot be overstated. Previous research has explored the use of surface modifiers (SMs), such as single-side fluorinated graphene, to enhance the thermodynamic stability of ion intercalation when applied atop few-layer graphene (FLG). As we seek alternatives to lithium-ion batteries (LIBs), earth-abundant elements like sodium and potassium have emerged as promising candidates. However, a comprehensive investigation into staging intercalation has been lacking thus far. By delving into staging assemblies, we have uncovered a previously unknown intercalation site that offers the most energetically favorable binding. Here, we study the first three elements in both alkali (Li, Na, K) and alkaline (Be, Mg, Ca) earth metals. Furthermore, the precise mechanism underlying this intercalation system has remained elusive in prior studies. In our work, we employed density functional theory calculations with advanced hybrid functionals to determine the electrical properties at various stages of intercalation. This approach has been proven to yield more accurate and reliable electrical information. Through the analysis of projecting density of states and Mulliken population, we have gained valuable insights into the intricate interactions among the SM, ions, and FLG as the ions progressively insert into the structures. Notably, we expanded our investigation beyond lithium and explored the effectiveness of the SM on ions with varying radii and valence, encompassing six alkali and alkaline earth metals. Additionally, we discovered that the number of graphene layers significantly influences the binding energy. Our findings present groundbreaking concepts for material design, offering diverse and economically viable alternatives to LIBs. Furthermore, they serve as a valuable reference for fine-tuning electrical properties through staging intercalation and the application of SMs.