  In this paper, we construct a Dirac star model composed of $|\kappa|$ pairs
of spinor fields. The azimuthal harmonic indeces $m$ of these spinor fields are
half-integers, and they satisfiy $-(|\kappa|-\frac{1}{2})\leq m \leq
|\kappa|-\frac{1}{2}$. When $\kappa=1$, it corresponds to the conventional
Dirac star model, formed by two spinor fields with $m=\frac{1}{2}$ and
$m=-\frac{1}{2}$. When $|\kappa|>1$, among these $|\kappa|$ pairs of spinor
fields, there exist spinor fields with azimuthal harmonic indices
$m>\frac{1}{2}$, and all spinor fields still conform to the same Dirac field
equation. Different families of solutions are distinguished by the value of
$\kappa$, so we named these solutions $\kappa$-Dirac stars. We obtain solutions
for $\kappa=\pm1,\pm2,\pm3,\pm4,\pm5,\pm6$ by using numerical methods.
Additionally, we compute their ADM mass $M$, Noether charge $Q$, and binding
energy $E$, and illustrate how these quantities change with the spinor field's
frequency $\omega$ for different $\kappa$. We observe significant differences
between solutions for $|\kappa|>1$ and the $|\kappa|=1$ case. Furthermore, we
provide the energy density distribution of the Dirac stars, wherein for
$|\kappa|>1$ scenarios, the Dirac stars exhibit a spherical shell-like
structure. Moreover, we employ three-dimensional diagrams to intuitively depict
how $\kappa$ influences the combination of spinor fields to form a spherically
symmetric configuration.
