  We have studied the Tb$_2$Sn$_2$O$_7$ frustrated magnet by neutron
diffraction under isotropic pressure of 4.6 GPa, combined with uniaxial
pressure of 0.3 GPa, in the temperature range 0.06 K$<$T$<$100 K. Magnetic
order persists under pressure but the ordered spin ice structure stabilized at
ambient pressure below 1.3 K partly transforms into an antiferromagnetic one.
The long range ordered moment at 0.06 K is reduced under pressure, which is
interpreted by a pressure induced enhancement of the spin liquid fluctuations.
Above the ordering transition, short range spin correlations are affected by
pressure, and ferromagnetic correlations are suppressed. The influence of
pressure on the ground state is discussed considering both isotropic and stress
effects.
