  We explore an extended quantum Rabi model describing the interaction between
a two-mode bosonic field and a three-level atom. Quantum phase transitions of
this few degree of freedom model is found when the ratio $\eta$ of the atom
energy scale to the bosonic field frequency approaches infinity. An analytical
solution is provided when the two lowest-energy levels are degenerate.
According to it, we recognize that the phase diagram of the model consists of
three regions: one normal phase and two superradiant phases. The quantum phase
transitions between the normal phase and the two superradiant phases are of
second order relating to the spontaneous breaking of the discrete $Z_{2}$
symmetry. On the other hand, the quantum phase transition between the two
different superradiant phases is discontinuous with a phase boundary line
relating to the continuous $U(1)$ symmetry. For a large enough but finite
$\eta$, the scaling function and critical exponents are derived analytically
and verified numerically, from which the universality class of the model is
identified.
