The non-centrosymmetric Weyl semimetal candidate, MoTe$_2$ was investigated through neutron diffraction and transport measurements at pressures up to 1.5 GPa and at temperatures down to 40 mK. Centrosymmetric and non-centrosymmetric structural phases were found to coexist in the superconducting state. Density Functional Theory (DFT) calculations reveal that the strength of the electron-phonon coupling is similar for both crystal structures. Furthermore, it was found that by controlling non-hydrostatic components of stress, it is possible to mechanically control the ground state crystal structure. This allows for the tuning of crystal symmetry in the superconducting phase from centrosymmetric to non-centrosymmetric. DFT calculations support this strain control of crystal structure. This mechanical control of crystal symmetry gives a route to tuning the band topology of MoTe$_2$ and possibly the topology of the superconducting state.
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