The ubiquity of distributed agreement protocols, such as consensus, has galvanized interest in verification of such protocols as well as applications built on top of them. The complexity and unboundedness of such systems, however, makes their verification onerous in general, and, particularly prohibitive for full automation. An exciting, recent breakthrough reveals that, through careful modeling, it becomes possible to reduce verification of interesting distributed agreement-based (DAB) systems, that are unbounded in the number of processes, to model checking of small, finite-state systems. It is an open question if such reductions are also possible for DAB systems that are doubly-unbounded, in particular, DAB systems that additionally have unbounded data domains. We answer this question in the affirmative in this work thereby broadening the class of DAB systems which can be automatically and efficiently verified. We present a novel reduction which leverages value symmetry and a new notion of data saturation to reduce verification of doubly-unbounded DAB systems to model checking of small, finite-state systems. We develop a tool, Venus, that can efficiently verify sophisticated DAB system models such as the arbitration mechanism for a consortium blockchain, a distributed register, and a simple key-value store.