  The interplay among anisotropic magnetic terms, such as the bond-dependent
Kitaev interactions and single-ion anisotropy, plays a key role in stabilizing
the finite-temperature ferromagnetism in the two-dimensional compound
$\rm{CrSiTe_3}$. While the Heisenberg interaction is predominant in this
material, a recent work shows that it is rather sensitive to the compressive
strain, leading to a variety of phases, possibly including a sought-after
Kitaev quantum spin liquid [C. Xu, \textit{et. al.}, Phys. Rev. Lett.
\textbf{124}, 087205 (2020)]. To further understand these states, we establish
the quantum phase diagram of a related bond-directional spin-$3/2$ model by the
density-matrix renormalization group method. As the Heisenberg coupling varies
from ferromagnetic to antiferromagnetic, three magnetically ordered phases,
i.e., a ferromagnetic phase, a $120^\circ$ phase and an antiferromagnetic
phase, appear consecutively. All the phases are separated by first-order phase
transitions, as revealed by the kinks in the ground-state energy and the jumps
in the magnetic order parameters. However, no positive evidence of the quantum
spin liquid state is found and possible reasons are discussed briefly.
