In recent decades, income and wealth inequality grew, educational attainment rose, and occupational hierarchies shifted to reflect changing job requirements. Because these four dimensions of class are intertwined---with higher education often leading to higher prestige jobs that generate higher incomes that augment wealth---rising inequality in one dimension may have increased polarization across multiple dimensions. Are people occupying increasingly similar positions across many class dimensions (wherein some enjoy high income, high wealth, high educational attainment, and high occupational prestige, while others occupy the bottom of all distributions)? We examine time trends and racial differences in this class crystallization via novel hierarchical covariance regression models. Preliminary results using PSID data suggest that class crystallization remained quite stable, partly because Black people's chances of occupying the bottom of multiple distributions declined, although their income, wealth, and prestige returns to education increased less than White people's, reflecting ongoing structural and interpersonal racism.