When only a few lower modes data are available to evaluate a large number of unknown parameters, it is difficult to acquire information about all unknown parameters. The challenge in this kind of updation problem is first to get confidence about the parameters that are evaluated correctly using the available data and second to get information about the remaining parameters. In this work, the first issue is resolved employing the sensitivity of the modal data used for updation. Once it is fixed that which parameters are evaluated satisfactorily using the available modal data the remaining parameters are evaluated employing modal data of a virtual structure. This virtual structure is created by adding or removing some known stiffness to or from some of the stories of the original structure. A 12-story shear building is considered for the numerical illustration of the approach. Results of the study show that the present approach is an effective tool in system identification problem when only a few data is available for updation.