This paper presents a parametric study conducted on five Steel Moment Frames (SMFs) varying in height (2-, 4-, 8-, 12-, and 20- story) to assess the interactive effect of the column base hysteretic behavior, continuous gravity columns and partially restrained gravity beam-column connections in their seismic performance. The frame response is examined through sophisticated Nonlinear Time History (NTH) and Nonlinear Static Pushover (NSP) analyses conducted as per FEMAp695 methodology. For each SMF, a range of base connection strengths (and their corresponding rotational stiffnesses) accompanied by different levels of gravity columns rigidity and gravity connection strengths are assigned, resulting in a total of 80 model simulations. Two collapse/failure limit states are formulated for the assessment 1) sidesway collapse defined as per FEMAp695; and 2) column-base connection failure, defined as base rotations exceeding a 0.05 rad threshold. Results from the simulations indicate that the gravity framing system profoundly affects the behavior of the SMFs analyzed by reducing their probability of collapse. In this manner, the seismic demands for the design of column-base connections can be reduced safely, incorporating their high deformation capacity as part of the energy dissipative mechanisms. Potential design implications are discussed, and limitations, as well as lines for future research, are outlined.