Body-centered multi-principal element alloys (BCC-MPEAs) based only on hydride-forming elements have low equilibrium plateau pressures during reaction with hydrogen and, consequently, high decomposition temperatures due to the high thermodynamic stability of related hydrides. In this work, we present a strategy to decrease the stability of the final hydrides formed in the BCC TiVNb alloy by simultaneous addition of two non-hydride forming elements, Cr and Al. The (TiVNb)100-x(CrAl)x alloys with x = 10, 20, 30, and 40 at.% crystallize as major BCC solid solutions with dendritic microstructures. Pressure-Composition-Temperature diagrams revealed that the combined addition of Cr and Al thermodynamically destabilizes the dihydride formation for x = 10 and 20 at.%. For higher Cr/Al contents the destabilization is too large to form stable hydrides under maximum 100 bar pressure. The absorption/desorption plateau pressure at room temperature for (TiVNb)80(CrAl)20 alloy are 9 and 0.6 bar, respectively, enabling a reversible capacity of about 0.8 H/M (1.4 wt%) at ambient conditions. The present results provide important insights into the effects of simultaneous Cr and Al additions in BCC-MPEAs and shed light on the design of new alloys with hydrogen absorption and desorption ability at ambient conditions.