  We study a three-level Dicke model in V-configuration under both closed and
open conditions. With independently tunable co- and counter-rotating coupling
strength of the interaction Hamiltonian, this model is a generalization of the
standard Dicke model that features multiple distinct parameter regimes. Based
on a mean-field approach and third quantization analysis, it is found that the
system exhibits rich quantum phase behaviours, including distinct superradiant
fixed points, multi-phase coexistence and limit cycle oscillation. In
particular, the cavity dissipation stabilizes a family of inverted spin
coherent steady states, whose stability region can be enlarged or reduced by
properly tuning the imbalance between the co- and counter-rotating
interactions. This property provide a conceptually new scenario to prepare
coherent atomic state with high fidelity.
