In this paper, we explore the power of the cosmic microwave background (CMB) polarization (E-mode) data to corroborate four potential anomalies in CMB temperature data: the lack of large angular-scale correlations, the alignment of the quadrupole and octupole (Q-O), the point-parity asymmetry, and the hemispherical power asymmetry. We use CMB simulations with noise representative of three experiments—the Planck satellite, the Cosmology Large Angular Scale Surveyor (CLASS), and the LiteBIRD satellite—to test how current and future data constrain the anomalies. We find the correlation coefficients ρ between temperature and E-mode estimators to be less than 0.1, except for the point-parity asymmetry (ρ = 0.17 for cosmic-variance-limited simulations), confirming that E-modes provide a check on the anomalies that is largely independent of temperature data. Compared to Planck component-separated CMB data (smica), the putative LiteBIRD survey would reduce errors on E-mode anomaly estimators by factors of ∼3 for hemispherical power asymmetry and point-parity asymmetry, and by ∼26 for lack of large-scale correlation. The improvement in Q-O alignment is not obvious due to large cosmic variance, but we found the ability to pin down the estimator value will be improved by a factor ≳100. Improvements with CLASS are intermediate to these.