Today's scientific simulations require a significant reduction of data volume because of extremely large amounts of data they produce and the limited I/O bandwidth and storage space. Error-bounded lossy compressor has been considered one of the most effective solutions to the above problem. In practice, however, the best-fit compression method often needs to be customized/optimized in particular because of diverse characteristics in different datasets and various user requirements on the compression quality and performance. In this paper, we develop a novel modular, composable compression framework (namely SZ3), which involves three significant contributions. (1) SZ3 features a modular abstraction for the prediction-based compression framework such that the new compression modules can be plugged in easily. (2) SZ3 supports multialgorithm predictors and can automatically select the best-fit predictor for each data block based on the designed error estimation criterion. (3) SZ3 allows users to easily compose different compression pipelines on demand, such that both compression quality and performance can be significantly improved for their specific datasets and requirements. (4) In addition, we evaluate several lossy compressors composed from SZ3 using the real-world datasets. Specifically, we leverage SZ3 to improve the compression quality and performance for different use-cases, including GAMESS quantum chemistry dataset and Advanced Photon Source (APS) instrument dataset. Experiments show that our customized compression pipelines lead to up to 20% improvement in compression ratios under the same data distortion compared with the state-of-the-art approaches.