  We theoretically study enhancement mechanisms of the Kondo effect in
multilevel quantum dots. In quantum dots fabricated on semiconductors, the
energy difference between discrete levels \Delta is tunable by applying a
magnetic field. With two orbitals and spin 1/2 in the quantum dots, we evaluate
the Kondo temperature T_K as a function of \Delta, using the scaling method.
T_K is maximal around \Delta=0 and decreases with increasing |\Delta|,
following a power law, T_K(\Delta)=T_K(0) (T_K(0)/|\Delta|)^\gamma, which is
understood as a crossover from SU(4) to SU(2) Kondo effect. The exponents on
both sides of a level crossing, \gamma_L and \gamma_R, satisfy a relation of
\gamma_L \gamma_R=1. We compare this enhanced Kondo effect with that by
spin-singlet-triplet degeneracy for an even number of electrons, to explain
recent experimental results using vertical quantum dots.
