Previous literature finds negative relationships between different socio-economic indicators and the completed fertility of women; however, these relationships might vary across cohorts. The current study asks whether adult women with different levels of completed fertility share similar socio-economic characteristics across cohorts, and whether exceptional parity level is related to social marginality. Using a sample of 11,809 women aged 40+ from the American Integrated Fertility Survey Series, we divide the women into four groups according to the exceptionality of their completed fertility level relative to the completed fertility of their birth cohort: 1) childless women; 2) women with low parity; 3) women with medium parity; and 4) women with high parity. Our results, using a multivariate multinomial regression, suggest that women with high parity are socially marginalized, across cohorts. We find that these women, when they are aged 40+, are on average less educated and have lower income. Moreover, they have lower income-to-poverty ratios. We further find that these women have higher number of siblings. These findings suggest that if there is an intergenerational transmission of preference for children, the social mobility of the offspring of these women might be lower relative to the other groups of mothers.