The pushover Enhanced DVA (E-DVA) method is based on the notion of elliptical response envelopes and allows several earthquake components to be taken into account simultaneously. The incremental quasi-static procedure for evaluating the seismic behavior of buildings accounting for their non-linear behavior multi-modal approach is presented. Inspired by the Direct Vectorial Addition (DVA) method, the load pattern for the pushover analysis is defined as a linear combination of modal load patterns. The novel approach improves the original DVA by introducing an operative procedure for the calculation of modal combination factors (called “alpha-factors”). The assumptions of the E-DVA allow asymmetric buildings to be analyzed accounting for torsion effects. Moreover, especially for multi-component earthquakes, the effect of higher modes is also taken into account. In addition, an approach is proposed for the identification of dominant modes and for their use into the definition of the pushover load pattern. Furthermore, this paper describes a method to obtain the equivalent Single-Degree-of-Freedom (SDoF) oscillator properties in the general multi-modal case under multi-component earthquake, with the corresponding factors for the capacity curve normalization. The definition of response spectrum for multi-component earthquakes is also given. For illustrative purposes, the E-DVA method is applied to a non-symmetric structure, and the main results are presented and discussed.