This paper proposes an extension of the National Growth Rate Method (NGRM) for making flexible estimation of internal migration into a region or a city, by incorporating the migration pattern as a function of time. Several single- and two-parameter families of functions of time have been suggested for the purpose. The estimation procedure is outlined along with the data requirement. The flexible NGRM, like its precursor of improved NGRM, can provide separate estimates for both the net migrants and their natural increase, which can be subjected to socio-economic analysis for the motivations or implications of migration.