  Type-II multiferroic materials, in which ferroelectric polarization is
induced by inversion non-symmetric magnetic order, promise new and highly
efficient multifunctional applications based on the mutual control of magnetic
and electric properties. Although this phenomenon has to date been limited to
low temperatures, here we report a giant pressure-dependence of the
multiferroic critical temperature in CuBr$_2$. At 4.5 GPa, $T_\mathrm{C}$ is
enhanced from 73.5 to 162 K, to our knowledge the highest value yet reported
for a non-oxide type-II multiferroic. This growth shows no sign of saturating
and the dielectric loss remains small under these high pressures. We establish
the structure under pressure and demonstrate a 60\% increase in the two-magnon
Raman energy scale up to 3.6 GPa. First-principles structural and magnetic
energy calculations provide a quantitative explanation in terms of dramatically
pressure-enhanced interactions between CuBr$_2$ chains. These large,
pressure-tuned magnetic interactions motivate structural control in cuprous
halides as a route to applied high-temperature multiferroicity.
