We report a new rapid-quench technique for the Kawai-type multi-anvil press: several important improvements were made to our previous design. As a result, we are able to routinely quench melts with low glass-forming ability and form glasses. Owing to the use of 3D-printed parts to supply the coolant, the new design is easier to assemble and demonstrates better temperature stability and cooling rate. It was also found that the cooling rate is both pressure- and temperature-dependent. The cooling rate increases with increasing pressure from 6700 °C/s at 1 GPa to 8200 °C/s at 5.5 GPa and decreases with increasing temperature at a rate of 550 °C s-1/100 °C. Taking these dependencies into account, the new rapid-quench design produces more than 15% higher cooling rate compared to the previous design. Moreover, enhancing coolant circulation, which was achieved by using tapered inner anvils with holes, additionally increases the cooling rate by about 4%. As the structure of the rapid-quench assembly differs dramatically from other existing designs, pressure calibration and temperature distribution in the experimental cell and sample capsule were determined for the first time. It was found that the first 0.6 MN of press load is not used to generate pressure due to the hard tungsten components in the assembly. At the current state-of-the-art, it is possible to routinely reach a pressure of 9 GPa and a temperature of 2200 K with the temperature variation not exceeding 70 K within the sample capsule.