Sporadic E (Es) layers exhibit strong intermittency and highly skewed intensity distributions, exerting significant impacts on high-frequency communication and navigation systems and posing challenges for data-driven prediction. Conventional single-stage regression models are often dominated by abundant non-event samples and therefore tend to underestimate Es intensity during occurrence periods. To address this issue, this study proposes a unified two-stage neural network framework that decouples the prediction of Es occurrence probability from the estimation of Es intensity. The model is trained using multi-station ionosonde observations, incorporating cyclic representations of seasonal and local time variations together with solar and geomagnetic indices and station-aware encoding to enable unified learning across multiple stations. Results show that the proposed two-stage framework achieves event-only MAE values of 0.53–0.76 MHz and RMSE values of approximately 1.0–1.4 MHz at most mid- and low-latitude stations, with larger errors at the high-latitude Casey station (MAE ≈ 1.45 MHz and RMSE ≈ 2.31 MHz). The consistently bounded MRE values (≈0.18–0.23) observed across multiple stations demonstrate that the framework effectively mitigates severe data imbalance and suppresses spurious high-intensity estimates under non-Es conditions.