Identifying eutectic compositions in multi-principal element alloys (MPEAs) is challenging in the absence of higher-order phase diagrams. The present study addresses this issue by proposing a revised criterion for eutectic-forming elements (EFEs), allowing elements to qualify as EFEs regardless of their binary eutectic-forming ability or enthalpy of mixing rank with other elements in the alloy system considered. Using this criterion, CALPHAD simulations in the Al-Co-Fe-Ni system identified a eutectic composition with Co as the EFE. Experimental validation confirmed that this composition exhibits a stable two-phase FCC plus BCC eutectic structure. This approach expands the design space for eutectic MPEAs, offering the potential for identifying new compositions.