Accurately localizing multiple sound sources in noisy and reverberant environments poses significant challenges. To address these, a two-stage framework is developed that integrates a multi-label, multi-class convolutional neural network (M-CNN) with a Bayesian prior. In the first stage, the M-CNN classifies directions of arrival (DOAs) based on the spherical harmonics decomposition (SHD) of signals captured by a spherical microphone array (SMA). In the second stage, a sparse Bayesian learning (SBL) algorithm is applied to the SHD signals using a high-resolution search grid, corresponding to the DOA classes identified in the first stage, to accurately localize multiple acoustic sources. The M-CNN model demonstrates robustness in noisy and reverberant conditions, while the SBL algorithm excels in high-resolution localization of sparse sources. This hybrid model enhances DOA estimation up to 1° accuracy and reduces root mean square error (RMSE) by 80%. Extensive simulations and real-world experiments validate the accuracy and performance of the proposed method.