This paper explores the use of sliding friction dampers (SFDs) as dissipative floor connectors to mitigate higher mode effects and earthquake-induced absolute acceleration demands on steel concentrically braced frame (CBF) buildings. The dampers connect each floor of the steel CBF system to the diaphragms of the gravity framing system (GFS) and they allow for a relative in-plane movement between the two systems. For this purpose, a design methodology is first proposed to define the activation forces in the SFDs so as to ensure damage-free seismic performance in the steel CBF and the diaphragms of the GFS. The efficiency of the design methodology is demonstrated through nonlinear response history analyses on a low- and high-ductility six-story steel CBF building. The simulation results suggest that (a) the determined activation forces of the SFDs are effective in mitigating higher mode effects and in preventing story drift concentrations regardless if capacity design is employed for the CBF system; (b) the absolute acceleration demands are reduced by approximately 50% relative to those in the rigid diaphragm counterpart. Similar reductions are achieved in the lateral drift demands of the GFS at seismic intensities with return periods of 475 and 2475 years. The reduction in the variability of seismic response, both in terms of absolute floor acceleration demands and story drift ratios (SDRs) in the CBF system, is noteworthy. Limitations as well as suggestions for future work are discussed.