  The excitonic insulator Ta$_2$NiSe$_5$ experiences a first-order structural
transition under pressure from rippled to flat layer-structure at Ps = 3 GPa,
which drives the system from an almost zero-gap semiconductor to a semimetal.
The pressure-induced semimetal, with lowering temperature, experiences a
transition to another semimetal with a partial-gap of 0.1-0.2 eV, accompanied
with a monoclinic distortion analogous to that occurs at the excitonic
transition below Ps. We argue that the partial-gap originates primarily from a
symmetry-allowed hybridization of Ta-conduction and Ni-valence bands due to the
lattice distortion, indicative of the importance of electron-lattice coupling.
The transition is suppressed with increasing pressure to Pc = 8 GPa.
Superconductivity with a maximum Tsc = 1.2 K emerges around Pc, likely mediated
by strongly electron-coupled soft phonons. The electron-lattice coupling is as
important ingredient as the excitonic instability in Ta2NiSe5.
