We present a new approach to estimate the dynamic stiffnesses of soil-foundation systems using earthquake induced response signals recorded on multi-story buildings with sparsely instrumentation. Identification of soil foundation dynamic stiffness parameters from real-life data, especially earthquake-induced response signals, is arguably one of the most challenging problems in structural/geotechnical earthquake engineering. This is because the said parameters are frequency-dependent, and the non-stationary input excitation is not measurable due to soil-structure interaction effects. It is possible to identify these parameters using recently developed blind source separation techniques, provided that a finite element model of the superstructure is available. However, developing and updating a finite element model is usually a laborious undertaking, and its success strongly depends on the spatial density of measurements. In the present study, we offer a new method that is based on the use of a Timoshenko beam model to represent the superstructure. In this method, key parameters of the Timoshenko beam model and those of its soil-foundation system are adjusted through a systematic procedure, until the systems' overall (flexible-based) modal properties match those identified from real-life data. The proposed method is robust against sensor sparseness, and yields accurate results even if the foundation rocking is not measured. The proposed procedure is first verified using a synthetic problem, and subsequently applied to real-life data recorded at the Millikan Library building, which is located at the Caltech campus in Pasadena, California.