The importance and role of a specific class of global transmissibility matrices (global TFs), here named response-based frequency response functions (R-FRFs), in the areas of the identification and continuous monitoring of structures, is discussed and expanded in the present paper. The R-FRFs, as specialized frequency response functions, have been recently introduced in the literature, and, as originally proved, they are able to inherently provide local poles related to the system under investigation, but, virtually, with a different set of boundary conditions; i.e. as if some of the original degrees of freedom, arbitrarily chosen by the analyst, were constrained to ground. In this paper, such a concept is extended, including mode shapes. Herein, we show that the R-FRFs are also able to provide local modes associated with the aforementioned local poles. In this regard, we provide a parametric model of the R-FRFs matrix, suitable for being tackled through frequency-domain estimators from the field of experimental and operational modal analysis, which let these additional modal parameters to be identified. Such a conceptual extension is carried out by both a theoretical and a numerical point of view. We process data sets from numerical and real-world experimental case studies and discuss the corresponding results. The estimated poles and modes are employed to detect structural modifications, in turn confirming the significance of response-based frequency response functions in the field of damage detection and structural health monitoring (SHM). •Response-based FRFs (R-FRFs) as a tool for analyzing the system in a local sense.•R-FRF modal decomposition in terms of perturbated original system modal parameters.•Modes of the original structure when subjected to virtual boundary conditions.•Modal parameter estimation based on frequency-domain estimator from the OMA field.•Sensitivity of R-FRF modal parameters for enhanced damage localization.