More than two decades of systematic investigation has made steady progress towards generating plate-like surface behaviour in models of vigorous mantle convection. Accordingly, properties required to obtain dynamic plates from mantle convection have become widely recognized and employed in both 2D and 3D geometries. Improving our understanding of the properties required to obtain durable (or replenishable) deep mantle features with LLSVP-like characteristics has received interest for a period with similar longevity. Investigation ultimately focusses on discovering the properties able to produce the presence of a detached pair of three-dimensional features, distinct from the ambient mantle. Here, we assume the LLSVPs have a chemical origin by incorporating a Compositionally Anomalous and Intrinsically Dense (CAID) mantle component comprising 2-3.5\% of the total mantle volume. The feedback between plate formation and the presence of a CAID mantle component is investigated in both 2D and 3D spherical geometries. We explore the impact of both an intrinsic contrast in density and viscosity for the CAID component, with the objective of finding system parameter values that encourage the formation of a pair of LLSVP-like assemblages and a surface that exhibits the principle features of terrestrial plate tectonics; including recognizable and narrowly focussed divergent, convergent and (in 3D) transform plate boundaries that separate 8-16 distinct plate interiors. We present the results of nine two-dimensional and eleven three-dimensional calculations and show that for some of the cases examined, a pair of CAID material provinces can be freely obtained in two-dimensional cases while maintaining a surface characterized by plate-like behaviour. However, specifying the same system parameters in the three-dimensional model does not readily yield a pair of provinces, during any period examined, for any values of the parameters investigated. Moreover, the inclusion of the CAID component in the mantle can affect the global geotherm so that in comparison to the surface behaviour obtained for the initial condition isochemical model, the surface behaviour of the cases incorporating the dense component are less exemplary of plate tectonics. In general, CAID material components that are 3.75\%-5\% denser than the surrounding mantle (at surface temperatures), and up to a factor of 100 times greater in intrinsic viscosity, form layers populated by voids, or nodes connected by tendril-like ridges that reach across the core-mantle-boundary, rather than distinct piles resembling LLSVPs. Due to its inherently heavy and stiff character, we find the CAID material becomes especially hot so that the temperature-dependence of its density and viscosity results in reduced distinction between the intrinsically dense assemblages and the ambient mantle in equilibrated systems. Accordingly, the CAID material forms masses on the CMB that are relatively less dense (1.25\%-3\%) and viscous than the adjacent mantle material, in comparison to the percentage differences obtained at common temperatures. We find that by adjusting our yield stress model to account for the influence of the CAID material on the geotherm, a highly satisfactory plate-like surface can be re-attained, however, the formation of a pair of LLSVP-shaped masses remains elusive.