Crystallographic texture generates anisotropy that is essential to many advanced ceramic applications. For microstructures where texture components have resulted from unique material processes, the measured texture is a superposition of these independent texture components, making it difficult to characterize these unique processes independently. For superposed crystallographic textures comprised of both a random and a textured component, the volume fraction bounds of the randomly oriented texture component can be determined from the minimum value of the superposed orientation distribution function (ODF). In such textures, the maximum pole density of the textured component ODF is shown to be a function of the minimum and maximum values of the superposed ODF. An illustration of the formalism is given for a textured bismuth titanate ceramic.