Magmatism is a known driver of flank instability at volcanoes where flank slip has been observed. Studies of instability at Kīlauea, Piton de la Fournaise, and Etna imply that long-term flank motion likely requires the presence of a layer accommodating the sliding, and a force, such as magma intrusion, that promotes slip. We present a parametric study using 2D Finite Element Models (FEMs), to assess how edifice aspect ratio, detachment fault geometry, asymmetric buttressing, and intrusion depth affect the potential for development of magma-driven flank instability at volcanoes. We quantify whether the tested conditions would favor flank slip based on the Coulomb Stress Changes (CSCs) associated with endmember scenarios and showcase the expected surface displacements for each scenario, to highlight their deviations from half-space models. Development of instability is more likely when flank slip is along a shallower-dipping receiver fault and the dike intrusion spans the edifice, regardless of edifice steepness. Another favorable scenario occurs in steep edifices with a steeply-dipping receiver fault when the dike is beneath the edifice. Buttressing slightly enlarges the region with conducive CSCs on shallow-dipping faults when the dike is within the edifice but shrinks the region with conducive CSCs in the steep edifice case with steeply-dipping faults. We also find that neglecting topography yields different magnitudes and extents of surface deformation, especially for steeper volcanic edifices. This topographical effect is more important when modeling horizontal displacements and stress fields induced by shallower intrusions.