Digital twins (DTs) are an emerging capability in additive manufacturing (AM), set to revolutionize design optimization, inspection, in situ monitoring, and root cause analysis. AM DTs typically incorporate multimodal data streams, ranging from machine toolpaths and in-process imaging to X-ray CT scans and performance metrics. Despite the evolution of DT platforms, challenges remain in effectively inspecting them for actionable insights, either individually or in a multidisciplinary, geographically distributed team setting. Quality assurance, manufacturing departments, pilot labs, and plant operations must collaborate closely to reliably produce parts at scale. This is particularly crucial in AM where complex structures require a collaborative and multidisciplinary approach. Additionally, the large-scale data originating from different modalities and their inherent 3D nature pose significant hurdles for traditional 2D desktop-based inspection methods. To address these challenges and increase the value proposition of DTs, we introduce a novel virtual reality (VR) framework to facilitate collaborative and real-time inspection of DTs in AM. This framework includes advanced features for intuitive alignment and visualization of multimodal data, visual occlusion management, streaming large-scale volumetric data, and collaborative tools, substantially improving the inspection of AM components and processes to fully exploit the potential of DTs in AM.