The present paper takes from the original outputonly identification approach named Full Dynamic Compound Inverse Method (FDCIM), recently published on this journal by the authors, and proposes an innovative, much enhanced version, in the description of more general forms of structural damping, including for classically adopted Rayleigh damping. This has led to an extended FDCIM formulation, which offers superior performance, on all the targeted identification parameters, namely: modal properties, Rayleigh damping coefficients, structural features at the element-level and input seismic excitation time history. Synthetic earthquake-induced structural response signals are adopted as input channels for the FDCIM approach, towards comparison and validation. The identification algorithm is run first on a benchmark 3-storey shear-type frame, and then on a realistic 10-storey frame, also by considering noise added to the response signals. Consistency of the identification results is demonstrated, with definite superiority of this latter FDCIM proposal.