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Two new refractory amorphous high-entropy alloys (RAHEAs) within the W--Ta--Cr--V and W--Ta--Cr--V--Hf systems were herein synthesized using magnetron-sputtering and tested under high-temperature annealing and displacing irradiation using \textit{in situ} Transmission Electron Microscopy. While the WTaCrV RAHEA was found to be unstable under such tests, additions of Hf in this system composing a new quinary WTaCrVHf RAHEA was found to be a route to achieve stability both under annealing and irradiation. A new effect of nanoprecipitate reassembling observed to take place within the WTaCrVHf RAHEA under irradiation indicates that a duplex microstructure composed of an amorphous matrix with crystalline nanometer-sized precipitates enhances the radiation response of the system. It is demonstrated that tunable chemical complexity arises as a new alloy design strategy to foster the use of novel RAHEAs within extreme environments. New perspectives for the alloy design and application of chemically-complex amorphous metallic alloys in extreme environments are presented with focus on their thermodynamic phase stability when subjected to high-temperature annealing and displacing irradiation.