We introduce the concept of an intra-lid cascaded multi-core vapor chamber (CMVC) for heat spreading in heterogeneous packages that simultaneously generate large total heat loads and high-power-density hotspots. Current thermal management strategies rely on spreading high local heat fluxes by conduction in the package lid, ultimately dissipating the total heat load using a mounted heat sink. Embedding vapor chambers within the lid is an attractive option to directly address intra-package hotspots, but their design must be reconsidered to simultaneously manage the large total heat load at low thermal resistance. We investigate the design of intra-lid vapor chambers, with water as the working fluid, for a representative device generating a total heat load of 476 W having a background heat flux of 0.75 W/mm², with hotspots of 8 W/mm² over a 1 mm² area. Conventional vapor chamber designs have a single vapor core, which requires thick evaporator wicks to avoid the capillary limit at high total heat loads; directly subjecting this thick wick to high heat flux hotspots imposes a large conduction resistance. To address this drawback, the CMVC concept comprises of a bottom-tier core having many small vapor cores that can each attenuate high heat flux hotspots before they pass through to the top tier, which has a single vapor core functioning as a conventional vapor chamber. Experimentally validated, reduced-order models predict that the CMVC offers an order of magnitude reduction in thermal resistance (0.66 K/W) compared to a solid copper benchmark (7.4 K/W) and conventional single-core vapor chamber (1.8 K/W) owing to a reduction in the conduction resistances across the internal wicks.