The next generation of superconducting magnets for the interaction regions of particle colliders, as well as for fast cycled accelerators, will be confronted with large heat loads. In order to improve the evacuation of heat from the Nb-Ti coil towards He-II bath, a porous (enhanced) all-polyimide cable insulation scheme was proposed recently. The first results were promising, featuring a larger permeability to helium with respect to existing schemes under low compressive stress. In this paper we present an extended experimental study of heat transfer through the Enhanced Insulation into He-II bath, and comparison to the standard LHC insulation, at different levels of applied pressure. The thermal coupling between adjacent cables was investigated, as well as the impact of a localized heat deposition versus a distributed one. The results of this study show that, up to high pressure levels, the enhanced insulation scheme can provide a major improvement of heat transfer compared to the standard scheme used in the main LHC magnets.