  We investigate the emergence of quantum critical points near a two-channel
Kondo phase by evaluating an $f$-electron entropy of a seven-orbital impurity
Anderson model hybridized with three ($\Gamma_7$ and $\Gamma_8$) conduction
bands with the use of a numerical renormalization group method First we
consider the case of Pr$^{3+}$ ion, in which quadrupole two-channel Kondo
effect is known to occur for the local $\Gamma_3$ doublet state. When we
control crystalline electric field (CEF) potentials so as to change the local
CEF ground state from $\Gamma_3$ doublet to $\Gamma_1$ singlet or $\Gamma_5$
triplet, we commonly observe a residual entropy of $\log \phi$ with the golden
ratio $\phi=(1+\sqrt{5})/2$, which is equal to that for three-channel Kondo
effect. This peculiar residual entropy is also observed for the case of
Nd$^{3+}$ ion, in which magnetic two-channel Kondo phase is found to occur for
the local $\Gamma_6$ doublet state. We envisage a scenario that the quantum
critical point characterized by $\log \phi$ generally appears between
two-channel Kondo and Fermi-liquid phases.
