If we have a many-particle System that is strongly correlated, the tunneling probability can significantly increase; see this article here:
The academic example of a computation of single particle amplitude could be generalized to tunneling of a system with high particle number. However, more particles means more collisions and these collisions make the quantum state decohere much faster. As a consequence of this, classical behavior will be observed.
Can quantum tunneling survive the decoherence process (that makes our everyday world looking classical) a lot easier than other quantum processes? I think yes, because radioactive decay is also based on quantum tunneling and does take place on a pressurized atmosphere under temperature of around 300K. Can dense systems (where the collision term in kinetic equations play an important role) that build up strong correlations make quantum tunneling much easier?