Low cost, scalability, potentially high energy density, and sustainability make organic magnesium (ion) battery (OMB) technologies a promising alternative to other rechargeable metal-ion battery solutions such as secondary lithium ion batteries (LIB). However, most reported OMB cathode materials have limited performance due to, in particular, low voltages often smaller than 2 V vs. Mg 2+ /Mg and/or low specific capacities compared to other competing battery technologies, e.g., LIB or sodium ion batteries. While the structural diversity of organic compounds and the large amount of possible chemical modifications potentially allow designing high voltage/capacity OMB electrode materials, the large search space requires efficient exploration of potential molecular-based electrode materials by rational design strategies on an atomistic scale. By means of density functional theory (DFT) calculations, we provide insights into possible strategies to increase the voltage by changes in electronic states via functionalization, by strain, and by coordination environment of Mg cations. A systematic analysis of these effects is performed on explanatory systems derived from selected prototypical building blocks: five-and six-membered rings with redox-active groups. We demonstrate that voltage increase by direct bandstructure modulation is limited, that strain on the molecular scale can in principle be used to modulate the voltage curve and that the coordination/chemical environment can play an important role to increase the voltage in OMB. We propose molecular structures that could provide voltages for Mg insertion in excess of 3 V.