  In a magnetic skyrmion phase, magnetic moments form vortex-like topological
textures which are of both fundamental and industrial interests. In
$\beta$-Mn-type Co-Zn-Mn alloys, chrial magnetic skyrmions emerge above room
temperature, providing a unique system for studying the skrymion physics and
exploring spintronics applications. However, the magnetic skyrmion phase is
typically confined in a narrow and limited temperature ($T$) and magnetic field
($H$) range. Here, we demonstrate that hydrostatic pressure can expand the
skyrmion phase in the $T-H$ phase diagram of single-crystalline
Co$_8$Zn$_8$Mn$_4$. At ambient pressure, signatures of skyrmions are seen
within $T\sim302-308$ K and $H\sim50-100$ Oe. Applying a moderate pressure of 6
kbar extends this range to $T\sim300-310$ K and $H\sim50-150$ Oe. However,
further escalation of pressure to 10 kbar results in a slight contraction of
the skyrmion phase. These findings underscore the sensitivity of the skyrmion
phase in Co$_8$Zn$_8$Mn$_4$ to external pressures, and hint at the potential of
strain engineering, particularly in $\beta$-Mn-type Co-Zn-Mn thin films, as a
promising avenue to customize the skyrmion phase.
