The modal-pushover-based-scaling (MPS) procedure has been developed for appositely selecting and scaling earthquake records for nonlinear response history analyses (RHAs) of multi-story symmetric-plan and single-story unsymmetric-plan buildings. This procedure is extended here to unsymmetric-plan buildings with significant torsional response under bi-directional earthquake excitations. The accuracy of the procedure is evaluated by using three-dimensional computer models of nine unsymmetric-plan buildings with 5, 10 and 15 stories. These models were subjected to nonlinear RHAs considering sets of seven far-field records selected and scaled according to the extended modal-pushover-based-scaling (EMPS) procedure. Structural responses were compared against benchmark values, defined as the median values of the engineering demand parameters (EDPs) due to a larger set of unscaled far-field records. Also examined here is the ASCE/SEI 7-10 scaling procedure for comparison purposes. This study clearly shows that the EMPS procedure provides much superior results in terms of accuracy (true estimates of expected median EDPs) and efficiency (reduced record-to-record variability of EDPs) than the ASCE/SEI 7-10 scaling procedure for far-field ground motions. Thus, the EMPS is deemed to be an appropriate procedure for nonlinear RHAs of multi-story unsymmetric-plan buildings.