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High-entropy alloys (HEAs) are a promising class of materials that can grant remarkable functional performances for a large range of applications due to their highly tunable composition. Among these applications, recently, <i>bcc</i> HEAs capable of forming <i>fcc</i> hydrides have been proposed as high-capacity hydrogen storage materials with improved thermodynamics compared to classical metal hydrides. In this context, a single-phase <i>bcc</i> (TiVNb)_0.90Cr_0.05Mn_0.05 HEA was prepared by arc melting to evaluate the effect of combined Cr/Mn addition in the ternary TiVNb. A thermodynamic destabilization of the <i>fcc</i> hydride phase was found in the HEA compared to the initial TiVNb. In situ neutron and synchrotron X-ray diffraction experiments put forward a <i>fcc</i> → <i>bcc</i> phase transition of the metallic subnetwork in the temperature range of 260–350 °C, whereas the H/D subnetwork underwent an order → disorder transition at 180 °C. The absorption/desorption cycling demonstrated very fast absorption kinetics at room temperature in less than 1 min with a remarkable total capacity (2.8 wt.%) without phase segregation. Therefore, the design strategy consisting of small additions of non-hydride-forming elements into refractory HEAs allows for materials with promising properties for solid-state hydrogen storage to be obtained.