In his seminal book "The Geometry of Thought", the cognitive scientist Peter Gardenförs puts forth the theory of Conceptual Spaces, as a geometric theory for understanding the cognitive structures that we can employ to: (i) provide an ontological interpretation for qualia and other results of sensory inputs; (ii) provide semantic referents for properties and concepts; (iii) explain certain aspects of logical and linguistic phenomena such as non-monotonic and context-dependent inference and analogical reasoning. Despite all its advantages, this theory has been criticized for its insufficient treatment of fundamental issue of identity of individuals and, related to that, its inability to recognize a heavily supported distinction existing in Philosophy of Language, Descriptive Metaphysics and Cognitive Psychology, namely, the distinction between Sortal and Characterizing Universals, as well the distinction between different types of modal classification involving universals (e.g., the Rigid/Anti-RigidDistinction). In this talk, we show how the theory of Conceptual Spaces can be extended with a richer Ontology of Universals and an associated theory of Intensional Logics with Sortal Quantification to address the aforementioned criticisms.