The current practice of designing for the most critical earthquake event expected during the design life of the structure does not account for the possibility of structure getting damaged due to the smaller events and being rendered unfit to survive the most critical event. This is particularly the case when no repairs are feasible after some or all of the smaller but damaging events. The safety of the structure in such cases may be ensured by suitably raising the design force level of the structure and thus by limiting the cumulative damage in the structure before the most critical event occurs. This study considers the estimation of required increase by modifying the concept of design force ratio (DFR) spectrum such that only the effects of multiplicity of events are taken into account. DFR represents the ratio of the design force level required for a given cumulative damage due to all events to that required for a given ductility demand during the most critical event. For more realistic estimates of the modified DFR, the existing formulation of estimating DFR spectrum is modified by generalizing the power spectral density function (PSDF)-based characterization of seismic hazard due to an event to apply for the oscillators of a wide range of damping ratios. The proposed ‘representative PSDF’ is based on suitably increasing the damping of the oscillator, depending on the definition of the strong-motion duration used. It is shown through a numerical study based on a hypothetical seismic region that the dependence of modified DFR on oscillator period may be ignored. Also, dependence on the sequence of events and on the directions of residual displacements is weak, and therefore, all residual displacements may be assumed in the same direction and all events may be assumed to occur in the increasing order of their damage-causing potential.