A method is described for stacking a plurality of cores. For example, one embodiment comprises: mounting an uncore die on a package, the uncore die comprising a plurality of exposed landing slots, each landing slot including an inter-die interface usable to connect vertically to a cores die, the uncore die including a plurality of uncore components usable by cores within the cores die; and vertically coupling a first cores die comprising a first plurality of cores on top of the uncore die, the cores spaced on the first cores die to correspond to all or a first subset of the landing slots on the uncore die, each of the cores having an inter-die interface positioned to be communicatively coupled to a corresponding inter-die interface within a landing slot on the uncore die when the first cores die is vertically coupled on top of the uncore die.