Subjective listening tests remain the golden standard for speech quality assessment, but are costly, variable, and difficult to scale. In contrast, existing objective metrics, such as PESQ, F0 correlation, and DNSMOS, typically capture only specific aspects of speech quality. To address these limitations, we introduce Uni-VERSA, a unified network that simultaneously predicts various objective metrics, encompassing naturalness, intelligibility, speaker characteristics, prosody, and noise, for a comprehensive evaluation of speech signals. We formalize its framework, evaluation protocol, and applications in speech enhancement, synthesis, and quality control. A benchmark based on the URGENT24 challenge, along with a baseline leveraging self-supervised representations, demonstrates that Uni-VERSA provides a viable alternative to single-aspect evaluation methods. Moreover, it aligns closely with human perception, making it a promising approach for future speech quality assessment.