In this paper, we introduce the Generalized Video Moment Retrieval (GVMR) framework, which extends traditional Video Moment Retrieval (VMR) to handle a wider range of query types. Unlike conventional VMR systems, which are often limited to simple, single-target queries, GVMR accommodates both non-target and multi-target queries. To support this expanded task, we present the NExT-VMR dataset, derived from the YFCC100M collection, featuring diverse query scenarios to enable more robust model evaluation.Additionally, we propose BCANet, a transformer-based model incorporating the novel Boundary-aware Cross Attention (BCA) module. The BCA module enhances boundary detection and uses cross-attention to achieve a comprehensive understanding of video content in relation to queries. BCANet accurately predicts temporal video segments based on natural language descriptions, outperforming traditional models in both accuracy and adaptability. Our results demonstrate the potential of the GVMR framework, the NExT-VMR dataset, and BCANet to advance VMR systems, setting a new standard for future multimedia information retrieval research.