  We consider excited configuration and multistate configuration of rotating
axion boson stars~(RABSs).RABSs are asymptotically flat, stationary, spinning,
horizonless solutions of Einstein-Klein-Gordon theory in which the scalar
potential depends on scalar field mass $\mu$ and axion decay constant $f_a$.
The excited RABSs have two types of solutions, including $^2S$ state and $^2P$
state. The rotating multistate axion boson stars~(RMABSs) consist of coupled
fundamental configuration and excited configuration, and also include two types
of solutions: $^1S^2S$ state and $^1S^2P$ state. Some differences between RABSs
models and rotating mini-boson stars models are discussed. We show the solution
space of these models for different values of decay constant $f_a$. We found
fundamental RABSs have a higher maximum mass than the excited state in the low
decay constant region. Moreover, the multistate configuration allows a higher
mass than both the fundamental configuration and the excited configuration at
the same frequency. We also found the RMABSs have the second branch in which
the ergo-region emerges. This means the second branch may be superradiant
unstable.
