Abstract: We have tuned the paramagnetic heavy Fermion (HF) system CeTiGe to a more magnetic state and toward quantum criticality (QC) by partially substituting La for Ce. The induced volume expansion leads to a pronounced decrease of the Kondo temperature (T_K), from ≈50 K in pure CeTiGe to less than 4 K at large La content. Since the former value is of the order of the crystal field splitting, while the latter is well below, the systems evolves from a large degeneracy N = 6 Kondo system at x = 0 to a conventional N = 2 Kondo system at x ≥ 0:8. There, the first excited crystal field doublets become apparent in the T dependence of the specific heat C_P(T) at an excitation energy D_CF ≈ 30 K. The reduction of the degeneracy is expected to enhance the decrease of T_K, explaining the strong reduction by more than one order of magnitude observed in this system. The decrease of T_K drives the system toward QC as evidenced by a divergence of C_P(T)/T and x(T) toward low temperatures in the x = 0:8 sample. © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.