  We report a systematic study on the growth conditions of Sn$_{1-x}$In$_x$Te
thin films by molecular beam epitaxy for maximization of superconducting
transition temperature $T_\mathrm{c}$. Careful tuning of the flux ratios of Sn,
In, and Te enables us to find an optimum condition for substituting rich In
content ($x$ = 0.66) into Sn site in a single phase of Sn$_{1-x}$In$_x$Te
beyond the bulk solubility limit at ambient pressure ($x$ = 0.5).
$T_\mathrm{c}$ shows a dome-shaped dependence on In content $x$ with the
highest $T_\mathrm{c}$ = 4.20 K at $x$ = 0.55, being consistent to that
reported for bulk crystals. The well-regulated Sn$_{1-x}$In$_x$Te films can be
a useful platform to study possible topological superconductivity by
integrating them into the state-of-the-art junctions and/or proximity-coupled
devices.
