Software vulnerability detection (SVD) aims to identify potential security weaknesses in software. SVD systems have been rapidly evolving from those being based on testing, static analysis, and dynamic analysis to those based on machine learning (ML). Many ML-based approaches have been proposed, but challenges remain: training and testing datasets contain duplicates, and building customized end-to-end pipelines for SVD is time-consuming. We present Tenet, a modular framework for building end-to-end, customizable, reusable, and automated pipelines through a plugin-based architecture that supports SVD for several deep learning (DL) and basic ML models. We demonstrate the applicability of Tenet by building practical pipelines performing SVD on real-world vulnerabilities.