Two modifications have been made to a miniature ceramic anvil high pressure cell (mCAC) designed for magnetic measurements at pressures up to 12.6 GPa in a commercial superconducting quantum interference (SQUID) magnetometer [N. Tateiwa et al., Rev. Sci. Instrum. 82, 053906 (2011); ibid. 83, 053906 (2012)]. Replacing the Cu-Be piston in the former mCAC with a composite piston composed of the Cu-Be and ceramic cylinders reduces the background magnetization significantly smaller at low temperatures, enabling more precise magnetic measurements at low temperatures. A second modification to the mCAC is the utilization of a ceramic anvil with a hollow in the center of the culet surface. High pressures up to 5 GPa were generated with the "cupped ceramic anvil" with the culet size of 1.0 mm.