A numerical scheme for stable and non-dissipative compressible flow simulations on hierarchical Cartesian grids is proposed. The scheme is based on the kinetic energy and entropy preserving (KEEP) schemes which were proposed recently. In previous studies, the KEEP schemes demonstrated more stable flow simulations, compared to typical kinetic energy preserving (KEP) schemes. An extension of the KEEP scheme is performed to satisfy conservation even at computational block boundaries associated with hanging nodes; the sum of the outflux from a fine grid block is the same as the influx to a coarse grid block, and the same is true for the flux exchange in the opposite direction. The extension of the KEEP scheme will be assessed by a numerical experiment at the conference.