  Unconventional superconductivity often couples to other electronic orders in
a cooperative or competing fashion. Identifying external stimuli that tune
between these two limits is of fundamental interest. Here, we show that
$c$-axis strain couples directly to the competing interaction between charge
stripe order and superconductivity in La$_{1.88}$Sr$_{0.12}$CuO$_4$ (LSCO).
Compressive $c$-axis pressure amplifies stripe order within the superconducting
state, while having no impact on the normal state. By contrast, strain
dramatically diminishes the magnetic field enhancement of stripe order in the
superconducting state. This observation hints to the existence of a ground
state without phase competition. As such, c-axis pressure is a promising tuning
parameter in the search for ground states where superconductivity adopts broken
translational symmetry from charge ordering phenomena.
