While much of the data available about the Earth pertains to the surface, there also exists a large amount of data available about the atmosphere and regions below the surface. Examples of such data include weather information, lithospheric properties such as velocity, aircraft and satellite flight paths, and underground utility networks. Flattening such volumetric data to the surface for integration with a traditional discrete global grid system (DGGS) discards the spatial relationship between data at different heights, and makes retrieval less efficient when only a certain vertical domain is needed. Because of this, a volumetric extension of this data structure is needed that allows proper indexing of data based on both its location and its altitude/depth. A sophisticated volumetric DGGS will have all the benefits of existing surface DGGS, but will also allow the vertical relationship between data to be inherently represented in the grid itself. We discuss various existing volumetric DGGS, and propose a collection of techniques that can be used to extend an existing DGGS to create a volumetric one that is consistent with the geometry and operations of the original. We also showcase a volumetric DGGS in action for representing different datasets at a variety of scales.