  In this study, we investigate muon $g-2$, $R_{K^{(*)}}$, and $R_{D^{(*)}}$
anomalies in a specific model with one doublet, one triplet, and one singlet
scalar leptoquark (LQ). When the strict limits from the $\ell' \to \ell
\gamma$, $\Delta B=2$, $B_{s}\to \mu^+ \mu^-$, and $B^+ \to K^+ \nu \bar\nu$
processes are considered, it is difficult to use one scalar LQ to explain all
of the anomalies due to the strong correlations among the constraints and
observables. After ignoring the constraints and small couplings, the muon $g-2$
can be explained by the doublet LQ alone due to the $m_t$ enhancement, whereas
the measured and unexpected smaller $R_{K^{(*)}}$ requires the combined effects
of the doublet and triplet LQs, and the $R_D$ and $R_{D^*}$ excesses depend on
the singlet LQ through scalar- and tensor-type interactions.
