Most social mobility studies take a two-generation perspective, in which intergenerational relationships are represented by the association between parents' and offspring's socioeconomic status. This approach, albeit widely adopted in the literature, has serious limitations when more than two generations of families are considered. In particular, it ignores the role of families' demographic behaviors in moderating mobility outcomes and the joint role of mobility and demography in shaping long-run family and population processes. This paper provides a demographic approach to the study of multigenerational social mobility, incorporating demographic mechanisms of births, deaths, and mating into statistical models of social mobility. Compared to previous mobility models for estimating the probability of offspring's mobility conditional on parent's social class, the proposed joint demography-mobility model treats the number of offspring in various social classes as the outcome of interest. This new approach shows the extent to which demographic processes may amplify or dampen the effects of family socioeconomic positions due to the direction and strength of the interaction between mobility and differentials in demographic behaviors. I illustrate various demographic methods for studying multigenerational mobility with empirical examples using the IPUMS linked historical U.S. census representative samples (1850 to 1930), the Panel Study of Income Dynamics (1968 to 2015), and simulation data that show other possible scenarios resulting from demography-mobility interactions.