The increasing volume of medical images poses challenges for radiologists in retrieving relevant cases. Content-based image retrieval (CBIR) systems offer potential for efficient access to similar cases, yet lack standardized evaluation and comprehensive studies. Building on prior studies for tumor characterization via CBIR, this study advances CBIR research for volumetric medical images through three key contributions: (1) a framework eliminating reliance on pre-segmented data and organ-specific datasets, aligning with large and unstructured image archiving systems, i.e. PACS in clinical practice; (2) introduction of C-MIR, a novel volumetric re-ranking method adapting ColBERT's contextualized late interaction mechanism for 3D medical imaging; (3) comprehensive evaluation across four tumor sites using three feature extractors and three database configurations. Our evaluations highlight the significant advantages of C-MIR. We demonstrate the successful adaptation of the late interaction principle to volumetric medical images, enabling effective context-aware re-ranking. A key finding is C-MIR's ability to effectively localize the region of interest, eliminating the need for pre-segmentation of datasets and offering a computationally efficient alternative to systems relying on expensive data enrichment steps. C-MIR demonstrates promising improvements in tumor flagging, achieving improved performance, particularly for colon and lung tumors (p<0.05). C-MIR also shows potential for improving tumor staging, warranting further exploration of its capabilities. Ultimately, our work seeks to bridge the gap between advanced retrieval techniques and their practical applications in healthcare, paving the way for improved diagnostic processes.