We discuss the possibility of having multiple Kaluza-Klein (KK) dark matter candidates which arise naturally in generic Type-IIB string theory compactification scenarios. These dark matter candidates reside in various throats of the Calabi-Yau manifold. In principle, they can come with varied range of masses in four-dimensions depending upon the hierarchical warping of the throats. We show that consistency with cosmological bounds and four-dimensional effective theory description imposes strong constraints on the parameter space and the geometry of the throats. With a rather model-independent approach, we find that the mass scales allowed for the KK dark matter particles in various throats can vary between 0.1 eV and 10 TeV, depending upon the throat geometry. Thus, there could be simultaneously more than one kind of cold (and possibly warm and hot) dark matter components residing in the Universe. This multiple dark matter scenario could weaken the bound on a conventional supersymmetric dark matter candidate and could also account for extra relativistic degrees of freedom in our Universe.