  We have studied the effect of pressure on the pyrochlore iridate
Eu$_2$Ir$_2$O$_7$, which at ambient pressure has a thermally driven insulator
to metal transition at $T_{MI}\sim120$\,K. As a function of pressure the
insulating gap closes, apparently continuously, near $P \sim 6$\,GPa. However,
rather than $T_{MI}$ going to zero as expected, the insulating ground state
crosses over to a metallic state with a negative temperature coefficient of
resistivity, calling into question the true nature of both ground states. The
high temperature state also crosses over near 6 GPa, from an incoherent to a
conventional metal, suggesting a connection between the high and the low
temperature states.
