  High-temperature superconducting cuprates respond to doping with a dome-like
dependence of their critical temperature ($T_{\mathrm{c}}$). But the family
specific maximum $T_\mathrm{c}$ can be surpassed by application of pressure, a
compelling observation known for decades. We investigate the phenomenon with
high-pressure anvil cell nuclear magnetic resonance (NMR) and measure the
charge content at planar Cu and O, and with it the doping of the ubiquitous
CuO$_2$ plane with atomic scale resolution. We find that pressure increases the
overall doping, as widely assumed, but when it enhances $T_\mathrm{c}$ above
what can be achieved by doping, it leads to a hole redistribution favoring
planar O. This is similar to the observation that the family-specific maximum
$T_\mathrm{c}$ also increases if the hole content at planar O is raised at the
expense of that at planar Cu. Thus, the pressure-induced enhancement of
$T_\mathrm{c}$ points to the same mechanism.
