Kondo-based semimetals and semiconductors are of extensive current interest as a viable platform for strongly correlated states in the dilute carrier limit. It is thus important to explore the routes to understand such systems. One established pathway is through the Kondo effect in metallic nonmagnetic analogs, in the so called half-filling case of one conduction electron and oneﾠ4fﾠelectron per site. Here, we demonstrate that Kondo-based semimetals develop out of conduction electrons with a low-carrier density in the presence of an even number of rare-earth sites. We do so by studying the Kondo materialﾠYb3Ir4Ge13ﾠalong with its closed-4f-shell counterpart,ﾠLu3Ir4Ge13. Through magnetotransport, optical conductivity, and thermodynamic measurements, we establish that the correlated semimetallic state ofﾠYb3Ir4Ge13ﾠbelow its Kondo temperature originates from the Kondo effect of a low-carrier conduction-electron background. In addition, it displays fragile magnetism at very low temperatures, which in turn, can be tuned to a Griffiths-phase-like regime through Lu-for-Yb substitution. These findings are connected with recent theoretical studies in simplified models. Our results can pave the way to exploring strong correlation physics in a semimetallic environment.