We propose an advance Steered Response Power (SRP) method for localizing multiple sources. While conventional SRP performs well in adverse conditions, it remains to struggle in scenarios with closely neighboring sources, resulting in ambiguous SRP maps. We address this issue by applying sparsity optimization in SRP to obtain high-resolution maps. Our approach represents SRP maps as multidimensional matrices to preserve time-frequency information and further improve performance in unfavorable conditions. We use multi-dictionary Sparse Bayesian Learning to localize sources without needing prior knowledge of their quantity. We validate our method through practical experiments with a 16-channel planar microphone array and compare against three other SRP and sparsity-based methods. Our multidimensional SRP approach outperforms conventional SRP and the current state-of-the-art sparse SRP methods for localizing closely spaced sources in a reverberant room.