  The recently published no-hair theorems of Hod, Bhattacharjee, and Sarkar
have revealed the intriguing fact that horizonless compact reflecting stars
{\it cannot} support spatially regular configurations made of scalar, vector
and tensor fields. In the present paper we explicitly prove that the
interesting no-hair behavior observed in these studies is not a generic feature
of compact reflecting stars. In particular, we shall prove that charged
reflecting stars {\it can} support {\it charged} massive scalar field
configurations in their exterior spacetime regions. To this end, we solve
analytically the characteristic Klein-Gordon wave equation for a linearized
charged scalar field of mass $\mu$, charge coupling constant $q$, and spherical
harmonic index $l$ in the background of a spherically symmetric compact
reflecting star of mass $M$, electric charge $Q$, and radius $R_{\text{s}}\gg
M,Q$. Interestingly, it is proved that the discrete set
$\{R_{\text{s}}(M,Q,\mu,q,l;n)\}^{n=\infty}_{n=1}$ of star radii that can
support the charged massive scalar field configurations is determined by the
characteristic zeroes of the confluent hypergeometric function. Following this
simple observation, we derive a remarkably compact analytical formula for the
discrete spectrum of star radii in the intermediate regime $M\ll
R_{\text{s}}\ll 1/\mu$. The analytically derived resonance spectrum is
confirmed by direct numerical computations.
