AbstractHigh-entropy alloys (HEAs) composed of multiple-principal elements with (nearly) equimolar ratio establish a new conceptual framework for alloy design and hold a promise for extensive applications in industry, akin to the controlled expansion alloys (CEAs), such as Invar alloys. Spontaneously, one question emerges - would it be possible to synthesize a novel class of alloys combining the virtues of both CEAs and HEAs? Here, we report the pressure-induced magnetovolume effect in the body-centered-cubic CoCrFeAl HEA coupled with magnetic phase transitions from ferromagnetic to paramagnetic, and to non-magnetic states, originating from the successive collapses of local magnetic moments of Co and Fe. The observed magnetovolume anomalies, occurring in a progressive way, tailor appreciably the coefficient of thermal expansion of CoCrFeAl. These results further strengthen HEAs’ anticipated potential for designing multifunctional materials in virtue of their multiple outstanding properties, and reveal possible routes for their future synthesis.