Sparse Matrix-Matrix Multiplication (SpMM) on GPU is critical to applications ranging from scientific simulations to Graph Neural Networks (GNNs) and Deep Neural Networks (DNNs). Modern GPUs offer diverse processing units, such as CUDA cores, Tensor Cores, and Sparse Tensor Cores. Many SpMM libraries have been built to harness those different types of processors. Although impressive performance has been reported by each, including cuSparse, Sputnik, CLASP, and Jigsaw, a systematic study in this work shows that no single library is a clear winner across all matrices and scenarios. Based on the empirical observations, this work proposes the first solution to synergize the various libraries to best harness the heterogeneous processors and the array of cutting-edge libraries. The solution is an extensible framework, namely SparseX, that can automatically select the best matrix multiplication library (and types of processors) on the fly for a given sparse matrix on a GPU through an agile accurate predictive model. Experiments show that SparseX can speed up sparse matrix multiplications on thousands of real-world matrices significantly over the SOTA GPU libraries, achieving significant speedups (e.g., as much as 95.34x over cuSparse). Its extensible design makes it easy to be extended to cover new libraries and hardware architectures.